Pharmaceutical Engineering

Introduction

Pharmaceutical engineering involves the study of industrial processes usually carried out in pharmaceutical and allied industries. In pharmaceutical formulation industries the raw materials are converted into dosage forms. In bulk manufacturing industries pharmaceutically important materials such as drugs and excipients are prepared. Whether it is formulation manufacturing or bulk drug/excipient manufacturing, various processes are performed using various equipments and machineries. For example, mixing tank or crystallizer, filtration machine, or tablet press, ointment mill, etc. are used. These are manufactured by engineering companies. As a user, if the industrial pharmacist does not know fundamentals of engineering processes and of the relevant equipments, it would be difficult to operate these machines and understand their operations.

Usually, each process or activity involves a number of steps and each step is carried out separately. Thus, the activities can be divided into two categories

•Unit process, and

•Unit operation

Unit Process

Unit process can be defined as an activity in which various steps or unit operations take place in sequences. Unit process may be physical or chemical. The unit operations in combination make the process success.

Physical Process

The processes which take place without chemical reaction, are called physical process. For example, recrystallization of salt. The operations sequentially performed are:

Chemical Process

The processes which take place through chemical reactions are called chemical process. For example, manufacture of paracetamol.

Unit Operations

A unit operation is a basic step in a process. Unit operations involve a physical change or chemical transformation such as crystallization, evaporation, filtration, polymerization, isomerization, and other reactions in a process of separation. For example, in milk processing, homogenization, pasteurization, and packaging are each unit operations which are connected to the overall process. A process may require many unit operations to obtain the desired product from the starting materials, or feedstocks.

Thus, unit operation refers to individual step of a chemical process. For example, making tablets by granulation is a process in which sieving of powders, mixing of powders, preparation of wet granules, drying of wet granules, size reduction, blending of dried granules, compression of granules in form of tablets are various unit operations (steps) are involved.

In a unit process a number of unit operations may take place simultaneously or in a sequential manner, mechanism of these operations is based on some fundamental laws. In pharmaceutical manufacturing industries following activities are the unit operation:

Size reduction: This operation is done to reduce the particle size of drug or processes drug to achieve appropriate size range suitable for particular dosage form. For example, to prepare emulsion or ointment, the drug should be finely powdered. For oral suspension, the size of drug should be of coarse powder. It is a physical process. The drug may be synthetic or extracted from plant or animal source.

Drying: Drug or excipient used to prepare dosage form should have limited moisture content. Similarly, while preparing bulk drug or excipients, the product is dried at suitable temperature, so that the product (drug or excipient) contain limited moisture content. For this purpose, drying operation is very much important in pharmaceutical manufacturing unit. To manufacture tablet by wet granulation method, the wet granules are dried to remove unwanted amount of moisture. The moisture or solvent is evaporated out from the solid surface on heating.

Evaporation: This operation is usually carried out to remove the solvent at a temperature below the boiling point of the solvent to be removed. It is a surface phenomenon. Hence, rate of evaporation is proportional to the surface area exposed to air. The extract prepared from plant is evaporated to make it concentrated.

Distillation: It is a unit operation carried out mainly for preparation of distilled water or for removal of the solvent other than water from the extract prepared from plant. The extract is distilled to concentrate the extract and to recover the solvent. This operation is commonly done to obtain essential oil from plant parts.

These operations are very much common in nature and extensively used in pharmaceutical, food, and chemical industries.

Basic Laws

Generally, the law of conservation of mass and the law of conservation of energy are applicable to every process. These laws are used in engineering in following ways:

1. Material balance (as per law of conservation of mass), and

2. Energy balance (as per law of conservation of energy).

Material Balance

This is governed by the law of conservation of mass which is stated as the material can neither be created, nor be destroyed, only it can be changed from one form to another. In other words, the total quantity of materials used as input in a particular process shall be equal to the total quantity of output material, provided there is no loss of material during processing.

Illustration:

Say, 5.0 kg of Material A,

0.75kg of Material B and

1.5 kg of Material C is being mixed in a mixer;

then, after mixing, the total mass of mixed materials would be = (5.0 + 0.75 + 1.5) kg = 7.25 kg, assuming that there is no loss of material during mixing or handling.

Now, if the total amount of mixture is found to be 7.23 kg, then 7.25 - 7.23 = 0.02 kg would be considered as handling loss. Theoretical output (yield) would be 7.25 kg and practical output (yield) is 7.23 kg.

Note:

1. The practical yield may be equal to the theoretical yield,

2. The yield may be less than the theoretical yield, indicating that there is loss of material during processing.

3. In case of radioactive process, the concept of material balance does not stand true.

Mole

In a chemical reaction, concentration of reactant(s) and product(s) are expressed in molecular units; that is, in gram terms of molarity, molality or mole fraction.

In material balance calculations moles is used to express the amount of reactant or product in a chemical reaction.

Mole of an individual component is the number of gram molecular weight present in a particular amount (g) of the substance. Thus, 2g of oxygen means mole of oxygen (molecular weight of oxygen is 32) and 5 g of carbon means moles of carbon (molecular weight of carbon is 12).

If in a reaction there are multiple reactants, gram-moles or moles of each reactant should be calculated, to be added to find out the total moles of reactant(s).

Molarity

Molarity of a particular solute of a solution is defined as the number of moles of solute present per kg of solvent.

Mole Fraction

The concentration of one of solute(s) in a solution (mixture) can be expressed as

Illustration

Say, 5.3 g of sodium chloride and 2.5 g of potassium chloride are present a mixture.

Number of moles of sodium chloride in the mixture = 0.90 [Molecular weight of NaCl is 58.5]

Number of moles of potassium chloride in the mixture = = 0.03 [Molecular weight of KCl is 74.55]

Say, these materials are present in 500 g of water.

Mole of water present in a mixture = = 27.78 [Molecular weight of water is 18]

Sum of the mole fractions of all the components must be equal to 1 (unity).

In this case, total mole fractions of all the components (sodium chloride, potassium chloride and water)

= 0.031 + 0.001 + 0.967 = 0.999 (approximately 1.0)

Energy Balance

Energy is the capacity to exercise a force through a distance and demonstrates itself in various forms. The unit of energy in SI system is J (Joules). Thus, the energy per unit mass is known as specific energy. The unit of specific energy is J/kg. Characteristics of energy are:

➢Energy cannot be destroyed, it has different forms such as mechanical, chemical, thermal, electrical, radiation.

➢Energy can be converted from one form to another,

➢Energy can be transferred or conveyed from one place to another,

➢Energy can be stored in various forms utilizing a working substance.

The first law of thermodynamics is the law of conservation of energy. It also states that energy can be transformed into work.

Thus, when one kind of energy is destroyed or consumed, an equal amount of another kind must be formed.

Some Basic Concept

Rate of a Process or Reaction

The rate of a chemical reaction can be realized and expressed by understanding the change of concentration of the reacting species with time. Thus, the rate of a reaction can be expressed mathematically as:

Where C is the concentration and dC is very small change in concentration at a time, dt. This concept of rate can be expressed in

That is, any action to happen there must be a sufficient reason (according to the Newton’s law of motion), behind the progress, the reason works as the driving force. For example, the flow of water or flow-current in a river depends on 1. the quantity-difference of water and 2. heightdifference between two locations of the river. If there is sufficient difference in height, water from higher site will flow to the lower site and if there is no continuous supply of water after certain, upper sites of the river will dry up. Similarly, if a metallic-spoon is left as such within a hot liquid, the end of the inside the air, become hot due to flow of heat from one end to the other end of the spoon. This happen because the material of construction of spoon is a good conductor of electricity and the temperature difference between two points at two ends of the spoon.

Steady State

Whether it is heat or water, it moves from its higher state (level) to lower state. The movement continues till both the states become same or until an equilibrium is reached. That is, heat will go on moving till the temperatures at two points of two ends remains different, with passage of time this difference of temperature will reduce and ultimately will become equal. Thus, the quantity of heat flowing (net flow of heat) from hot region to cold region will gradually reduce and finally become zero. This final state is called steady-state. If the movement of energy or material is considered two-way action, it is expressed by two arrows at opposite direction shown in figure below.

When the equilibrium is reached; that is, the rate of forward reaction becomes equal to that of backward reaction, it is considered to attain steady state. In other words, steady state of a reaction is a condition when the concentration of the reactants or products does not change with time. On the other hand, if the operating condition vary with time, in a system, the system is considered as unsteady state or state. For example, water is boiling in a container. Before boiling, heat was transferred from source to water in the container and the temperature of water is gradually being increased. At this condition the system (water being heated) is under unsteady condition. Once the temperature of water is raised to the boiling point of water, water starts boiling. At this condition, no virtual movement of heat will take place from source to water, a dynamic equilibrium is attained. This condition is said to be steady state. Provided that the pressure above the water remains same.

Units, System and Conversion

Physical quantity measured must have a particular unit. The units may be length, mass, temperature, time or any other. For example, acceleration is the rate of change of velocity  ft/sec² or cm/sec²or momentum is the product of velocity, v and mass, m (mv) gm.cm/sec or lb. ft/sec. In engineering, different units are used even when only one system, either the metric or the British system, is commonly used. Thus, conversion of one simple unit, say 1 cm to another unit, say inch is required either by dividing or multiplying by a conversion factor.

Dimension requires measurement; measurement requires expression of the measured quantity using relevant unit; unit refers to the system; for better understanding conversion of the measured quantity should be converted to required system.

There are three systems used to measure a quantity.

1. CGS (Centimeter-Gram-Second) system, also known as metric system

2. FPS (Foot-Pound-Second) system, also known as British system

3. MKS or SI (Meter- Kilogram-Second) system, also known as Modern system.

Fundamental quantities measured are length, mass and time. In different systems, their values are different. The units used to express in a particular system may be divided into two categories:

1. Primary units: The units mentioned in any system to express the physical quantities such as length, mass and time are called fundamental or primary units . For example, cm-g- sec. or m-kg-sec.

2. Derived units: Certain physical quantities are expressed in terms of derived from fundamental units; for example, area and volume are derived from length unit, momentum from mass, length and time; density from mass and volume, etc. These units are called derived units or secondary units .

Physical quantities have two parts -

•Number such as one, two, three, four, etc.

•Unit indicating the system used to measure the quantity such cm/m/ft etc.

Combination of both indicates the actual value.

Illustration

Say mass of a liquid is 25g, it occupies a space measuring 2cm × 2cm × 5cm. That is, the volume of 25g of the liquid is 20cubic.cm or 20ml.

Then, the density of the liquid would be = = 1.25g/ml (derived unit)

Basic units in different systems are shown below in tabular form.

It is necessary to know the different units in different system and use a particular system for units. Some of the most commonly useful derived units in SI system are shown below

Conversion of Units

Conversion of units from CGS system to British system and vice versa

Gas Laws

Usually ideal gas law is expressed as: PV = nRT; where P is pressure, V is the volume, T is absolute temperature (ºK = ºC + 273.1 or ºRankine = ºF + 459.6), R is the universal gas constant, n is the number of moles of gas.

Although this gas law (ideal gas law) does not apply everywhere (particularly, to any real gas); in general, the law is most commonly used for engineering calculation and the law gives sufficiently correct answers in most of the cases. The law tells that

1. The volume of a gas is directly proportional to the number of moles of the gas present,

2. The volume is directly proportional to the absolute temperature,

3. The volume is inversely proportional to the pressure.

To calculate the volume of a gas at different temperature and pressure, the statement 2 and 3 become very necessary. The above gas equation can be written as;

Where V1is the volume of a gas at temperature T1 and pressure P1; the volume changes to V2 when the temperature changes to T2 under the pressure P2. Thus, if the value of the temperatures are known and any of the pressures and corresponding volume of the gas is known, then other volume can be easily calculated.

Illustration

Say, the volume of a gas changes from 250 cc to 325 cc, the temperature changes from 25oC to 35oC, if the initial pressure is 1 atm, find out the final pressure.

Thus, P1 = 1 atm = 76 cm of Hg

T1 = 25 + 273 = 298ºK

T2 = 35 + 273 = 308ºK

V1 = 250 cc,

V2 = 325 cc

P2=?

We know that,

Or,

So,

Mole Volume

According to the ideal gas equation, PV = nRT, one mole of a gas under particular temperature and pressure always occupies a definite volume irrespective of the nature of the gas. This volume is called the mole volume.

1-gram mole of an ideal gas occupies 22.41 lt at 0ºC and 1 atm (76 cm of Hg) pressure.

1 lb mole of an ideal gas occupies 359 c ft at 32ºF and 76 cm of Hg pressure.

Dalton’s Law of Partial Pressure

According to Dalton’s law, the total pressure exerted by a mixture of ideal gases shall be equal to the sum of the pressures that would be exerted by each of the gases if it alone were present and occupied the total volume. Amagat’s law of partial volume is similar to Dalton’s law. Amagat’s law states that in a mixture of ideal gases, each gas can be considered to occupy a fraction of the total volume equal to its own mole fraction and to be at the total pressure of the mixture. Thus, in a mixture of ideal gases each one of the mixtures occupies the entire volume at its own partial pressure, or a combination of partial volumes of the individual gases. Each partial volume is taken at the total pressure. As in the case of a pure gas, one lb mole is that weight of a gas mixture that will occupy 359 cft under one atmospheric pressure at 32oF. This may be called average molecular weight of the gas. From this statement of relationship, it can be stated that in a mixture of ideal gases

Volume % = Pressure % = Mole %

For example, air contains 79% of nitrogen and 21% of oxygen by volume. That is, under a pressure P atm, one cu. ft of air may be considered to be a mixture of 0.21 cu. ft of O2 at P atm and 0.79 cu. ft of N2 at P atm. It can also be considered as a mixture of 1 cu. ftof O2 at 0.21 P atm and 1 cu. ft of N2 at 0.79 P atm;% of total pressure is due to N2.

Thus, 1 mole of air contains 0.21 mole of O2 and 0.79 mole of N2 at all temperatures and pressures.

Exothermic and Endothermic Reactions

In chemical reactions or processes, heat may be evolved or absorbed. The reactions which generate heat, are called exothermic reactions; while the reactions absorb heat are called endothermic reactions. For example, sodium hydroxide when dissolved in water, heat is produced. While ammonium chloride is dissolved in water, it absorbed heat. The ∆H becomes positive in case of exothermic reactions and negative in case of endothermic reactions. In the reaction of one mole of solid carbon (in form of graphite) reacting with one mole of oxygen (gas), one mole of carbon dioxide (gas) is formed (C + O2 = CO2) and the standard heat of this reaction, ∆H is - 94.052 kcal at 25ºC. The negative sign indicates that the heat is evolved in the reaction (exothermic reaction). This means that the reactants, carbon and oxygen, contain 94.052 kcal in addition to the product, one mole of carbon dioxide. This heat is evolved during the reaction. If this reaction is reversed, that is, one mole of carbon dioxide (gas) is converted into one mole of carbon (solid) and one mole of oxygen (gas), the reaction will absorb the same amount of heat 94.052 kcal. Thus, the reaction would be endothermic one and ∆H would be positive.

Hess’s Law of Heat Summation

Hess demonstrated that since ∆H depends only on the initial and final states of a system, thermodynamic chemical equations for several steps in a reaction can be added or subtracted to obtain the overall heat of reaction. This principle is called Hess’s law of heat summation. This principle is used to obtain the heat of reactions that cannot be easily measured directly. If a reaction cannot be performed in a calorimeter, the ∆H25ºC for the reaction can be obtained as indicated below:

If the eqn.2 and its heat of combustion are subtracted from the eqn.1and its heat of combustion, we get

Hess’s law of heat summation may also be defined as: If a chemical change take place in two or more different ways, then in the total change, the amount of heat absorbed or evolved may be same; it does not depend on the method by which the change has been carried out. Thus, thermochemical reactions may be added or subtracted.

Dimensional Analysis

There are some problems which cannot be solved completely either by theoretical or mathematical methods, these require empirical experimentation. For example, the pressure of a liquid is reduced due to friction during the flow of a liquid through a long, straight, round, smooth pipe due to the following factors:

➢Length and diameter of the pipe,

➢Density of the liquid flowing,

➢Viscosity of the liquid flowing,

➢Rate at which the liquid flows,

If any one of these factors varies, the pressure drop will also change. The empirical method to get an equation that can correlate the pressure drop with the effects of all these factors, is that the effect of each factor on the pressure drop is to be determined separately. The effect one factor is to be determined by keeping other factors constant. This process is very laborious and it is very difficult to obtain a useful relationship by correlating all the results obtained.

Thus, intermediate between complete mathematical development and total empirical studies, there is a method called dimensional analysis. It is based on the fact that, if a theoretical equation exists among the variables that affect a physical process, that equation must be dimensionally homogeneous. As such it is possible to group the factors affecting the process into smaller number of dimensionless groups and these groups enter the final equation, not the factors separately. The benefit of this method is to reduce drastically the number of independent variables that effect the problem. However, dimensional analysis does not bring about a numerical equation and experiment is necessary to complete the solution to the problem.

Dimensional analysis shows that the variables must enter the final equation. In the above example, the variables shown are diameter of the pipe (D), velocity of the liquid (v), density (ρ) and viscosity of the liquid (η) must appear as a dimensionless group

A dimensional analysis cannot be made unless the physics of the process is known sufficiently to decide which factor would be important in the problem and what physical laws would be involved in a mathematical solution if one were possible. The method used to construct a dimensionless equation is important in research and development activities.

Dimensionless Groups

By use of dimensional analysis and other means, various important dimensionless groups have been developed. For example, Reynolds number

For a particular case, the numerical value of a dimensionless group does not depend on the unit of primary quantities present in the group, provided that consistent units are used within that group. However, the units used in one group may not be same and consistent with those used in other groups. For example, meters are used in one group while feet can be used in another group.

Use of Mathematical Methods

In the treatment of unit operations following mathematical methods are used:

1. Graphic method of integration (Graphical integration)

2. Graphical treatment of exponential functions.

1. Graphic method of integration (Graphical integration): In this method, integral calculus used shows that the value of a definite integral represents the area bounded by the curve of f(x) vs x, the ordinates x = x1and the x= x 2 and the x axis. Any definite integral can therefore be calculated numerically by plotting f(x) vs x, drawing two vertical lines corresponding to the limits, and the area is determined between the curve, the limits and the x axis, as shown below in the figure, without using the table. Thus, in the figure, if the curve MNOPQR expresses the plot of f(x) against x. If the lines MT and RS represent the values of x 1 and x 2 respectively, the complete area MNOPQRST becomes integrated value.

The area may be determined by splitting it into a series of rectangles such as the one shown cross-hatched in the figure.

The height of this rectangle is such that the area of the small triangle omitted between the rectangle and the curve is almost equal to the area of the small cross-hatched triangle within the rectangle above the curve. This can be observed by the naked eye. The area desired is thus, the sum of all such rectangles as the one shown in below.

Mean values: It becomes necessary to use the average values in many engineering calculations. In fact, averaging of values of some variables such as density, viscosity, velocities, etc. are required to obtain a reliable result. In some cases, averaging cannot be done easily; particularly, where the changes of the variable are represented by;

In such cases, the average value of y is calculated when x changes from x1 to x2 as follows

The equation 2 can be used when f(x) can be expressed by a mathematical function. In such case, formal integration should be used. If the relationship is known only as a curve and equation of the curve (the form of f(x)) is unknown, then the methods of graphic integration, must be used.

2. Exponential Equations and log-log plots

In many cases, experimental data including the variables x and y fit an equation of the form

where a and n are constants. It is possible to duplicate many curves by an equation of the type:

In many cases, the eqn. 4 can fit more accurately than the eqn. 3. Yet, the following eqn.3 can fit many experimental data closely enough to permit its use; this can be explained below. The constants of eqn.3 can be determined quickly. On the other hand, fitting the eqn.4 to experimental data is a tedious process and often requires the use of a large number of terms.

The eqn.3 may be rewritten as:

If log x is plotted against log y, the eqn.5 is the equation of a straight line with a slope of n and log a is the intercept, when x = 1. It is possible to plot log y against log x. However, for this purpose log-log paper can be used. The disadvantage of the logarithmic plot is that the scales normally used cannot be read too closely. In most cases, the points can be plotted with an accuracy comparable to the accuracy of normal engineering data. Advantage of log-log plots is that deviations from a curve of a given distance represent deviations of a constant per cent of the total value of the variable at that point, irrespective of the part of the plot in which they may lie.

CHAPTER 1

Flow of Fluid

Types of Manometers, Reynolds Number and its Significance, Bernoulli’s Theorem and its Applications, Energy Losses, Orifice Meter, Venturi Meter, Pitot Tube and Rotameter.

Types of Manometers

Manometer is one of the earliest devices used for measuring fluid pressure difference consisting of a hollow U-tube having one or more fluid (may be liquid or gas) of different specific gravities. It can provide a very accurate result. A U-tube manometer is recognized by NIST as a primary standard due to its inherent accuracy and simple operation. The manometer has no movable parts that can subject to wear. Manometers works on the Hydrostatic Balance Principle: a liquid column of known height will exert a known hydrostatic pressure when the weight per unit volume of the fluid is known. The fundamental relationship for pressure expressed by a fluid column is:

Where

p is the differential pressure,

P1 is the pressure at the low-pressure connection

P2 is the pressure at the high-pressure connection 

ρ is the density of the liquid 

g is acceleration due to gravity, and 

h is the height of the liquid column

All forms of manometers such as Piezometer, U-tube manometers, differential manometer, well-type, and inclined, etc. contain two liquid surfaces. Pressure determinations are made by how the fluid moves when pressures are applied to each surface. For gauge pressure, P2 is equal to zero (atmospheric reference), simplifying the above equation to

p = ρhg

In manometer, a known pressure (which is generally atmospheric pressure) is applied to one end of the manometer tube and the unknown pressure (to be determined) is applied to the other end.

The manometers measure the differential pressure; that is, only the difference between the two pressures. There are primarily four types of manometers:

1. Simple u-tube manometer - Piezometer

2. Differential U-tube manometers

3. U-tube with one leg enlarged (Well type manometer), and

4. Inclined U-tube manometer

The U-tube manometer may be of three types:

(a) Two fluid U-tube manometer,

(b) Four-fluid U-tube manometer, and

(c) Differential U-tube manometer

1. Simple u-tube manometer - Piezometer: It is used to measure the pressure in a static fluid by using the height of a column of a liquid as shown in  Figure 1.1.

Pressure at A = Pressure at B

 = p.g.h

Where, ρ is the density of the liquid

g is acceleration due to gravity

h is the height of the liquid column

Fig. 1.1 Piezometer

2. Differential U-tube manometers: The principles of manometry can be easily established in the U tube manometer shown in  Figure 1.2.  It is simply a glass-tube bent to form the letter U and partially filled with a liquid. If both the legs of the manometer are kept open to atmosphere or exposed to the same pressure, the levels of the liquid remain exactly on the same line or with a zero difference. As illustrated in  Figure 1.3 , if the pressure is more to the left side of the apparatus, the fluid level comes down to a lower level in the left leg and raises in the right leg. The fluid moves until the weight of the fluid as indicated in figure exactly balance the pressure. This is known as hydrostatic balance. The height of fluid from one side to the other is the actual height of fluid opposing the pressure. The pressure is always indicated by the height of fluid regardless of the shape or size of the tubes, as illustrated in  Figure 1.3.  Manometers in  Figure 1.3  are open to atmosphere on both legs indicating the fluid level in both legs. Because of the variations in the volume of the manometer legs, the distances moved by the fluid columns are different. However, the total distance between the fluid levels, H, remains identical in all the manometers.

Fig. 1.2 U-tube manometer

Fig. 1.3 U-tube manometer

Fig. 1.4 U-tube manometer

3. U-tube with one leg enlarged (Well type manometer): To provide convenience and to meet other requirements this type of manometer has been used. The well-type manometer is one of the various types of manometers. The schematic diagram of this type of manometer has been shown in  Figure 1.5.  The cross-sectional area of one leg of the manometer is many times larger than that of the other leg. The leg with a larger area is called the well. As pressure is applied to the larger leg, the fluid moves down compared to the increase in height of the smaller leg.

Fig. 1.5 Well type manometer

The true pressure reading follows the principles, previously described and is measured by the difference between the fluid surfaces h. As the pressure is applied at there must be some drop in the well level from O to X. This is readily compensated for by spacing the scale graduations in the exact amount required to correct for this well drop. To ensure the accuracy of this correction, the well area and internal diameter of the indicating tube must be carefully controlled.

Thus, the well type manometer offers itself to be used with direct reading scales graduated in units for the process or test variable involved. lt does require certain operational restrictions not found on the U-tube. A pressure higher than atmospheric pressure is always connected to the well; a pressure lower than atmospheric is always connected to the top of the tube. For a differential pressure, the higher pressure is connected at the well. A raised well manometer, however, allows both gauge and vacuum measurements off of the well port.

4. Inclined U-tube manometer: In many cases, accurate measurement of low pressure such as drafts and very low differentials are required. To handle these applications better the manometer is arranged with the indicating tube inclined, as shown in  Figure 1.6.  It provides better resolution. This arrangement can allow 12 of scale length to represent 1 of vertical liquid height. With subdivisions of scale, even up to a pressure of 0.00036 psi (one-hundredth of an inch of water) can be read.

Fig. 1.6 Inclined U-type manometer

Absolute Manometer

Absolute zero pressure refers to the pressure at a perfect vacuum. In an absolute pressure manometer, the pressure being measured is compared to absolute zero pressure in a sealed leg above a mercury column, as shown in Figure 1.7. The term absolute zero pressure is derived from the definition, that is, a perfect vacuum is the complete absence of any gas. The most common form of sealed tube manometer is the conventional mercury barometer used to measure atmospheric pressure. Mercury is the only fluid used in this application. In this type of manometer, there is only one connection from which both pressures above atmospheric pressure and pressure below atmospheric can be measured. Absolute manometers are available in well type or U tube configurations.

Fig. 1.7 Absolute manometer

Indicating Fluid

The sensitivity, range, and accuracy of the manometer can be improved by selecting an appropriate indicating fluid. Indicating fluids are available with densities varying from 0.827 g/cm³ (Red Oil) to 13.54 g/cm³ (Mercury). The pressure range would become three times greater and the resolution would be one third as great if an indicating fluid is three times heavier than water. If the density of an indicating fluid is less than water, the pressure range will decrease and the resolution (sensitivity) will increase. Thus, for a given size of the instrument, the pressure range can be increased by using a fluid with higher density and reduced by using a fluid with lower density.

Correction of the Manometer

Manometry measurements depend on both density and acceleration due to gravity. The values of the density and acceleration due to gravity are not always constant. Density is a function of temperature, and acceleration due to gravity is a function of latitude and elevation. Due to this relationship, specific ambient conditions must be selected as standard, so that a fixed pressure can be maintained.

Standard conditions for mercury: Density of mercury at 0ºC is 13.5951 g/cm³;

Acceleration due to gravity at sea level and at 45.544º latitude is 980.665 cm/sec²

Standard conditions for water:

Density of water at 4ºC is 1.000 g/cm³;

Acceleration due to gravity at sea level and at 45.544º latitude is 980.665 cm/sec²

Generally, the manometers may be read outside standard temperature and acceleration due to gravity and corrections should be made to improve the accuracy of a manometer reading at any given condition.

Correction of Fluid Density

Manometers indicate the correct pressure at only one temperature. This is because the indicating fluid density changes with temperature. If water is the indicating fluid, an inch scale indicates one inch of water at 4ºC only. On the same scale, mercury indicates one inch of mercury at 0ºC only. A reading using water or mercury taken at 20ºC (68º F) is not an accurate reading. The error introduced is about 0.4% of reading for mercury and about 0.2% of reading for water. Since manometers are used at temperatures above and below the standard temperature, corrections are needed. A simple way of correcting for density changes is to ratio the densities. At a particular place where the value of g is constant,

(Standard) ρcghc = (Ambient) ρgh

Where,

ρc = Density of indicating fluid at standard temperature,

hc = Corrected height of the indicating fluid at standard temperature,

h = Height of the indicating fluid at experimental temperature, and

ρ = Density of indicating fluid at the experimental temperature

This method is very accurate when density-temperature relations are known. Data is readily available for water and mercury.

The density (g/cm³) of mercury can be corrected as a function of temperature (0ºC) as

13.556786 [1 - 0.0001818(T - 15.5556)]

Density (g/cm³) of water can be corrected as a function of temperature (0ºC) as 0.9998395639 + 6.798299989 × 10-5 (T)

- 9.10602556 × 10 -6(T²) + 1.005272999 × l0 -7(T³) -

1.126713526 × 10 -9 (T⁴) + 6.591795606 × l0 -12(T⁵)

Reynolds Number

The Reynolds