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Mar 23, 2013, 4:04:53 AM3/23/13

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3.4 PRESSURE

3.4a Fluid Pressure and Hydrostatic Head

Pressure is the ratio of a force to the area. Accordingly, pressure units are force units divided by area units (e.g., N/m`, dynes/cm2, and lbf/in.2 or psi). The SI pressure unit, N/m2, is called a pascal (Pa).

Consider a fluid (gas or liquid) contained in a closed vessel or flowing through a pipe, and suppose that a hole of area A is made in the wall of the containing vessel, as in Figure 1. The fluid pressure may be defined as the ratio F/A, where F is the minimum force that would have to be exerted on a frictionless plug in the hole to keep the fluid from emerging.

Suppose a vertical column of fluid is h(m) high and has a uniform cross-sectional area A(m2). Further suppose that the fluid has a density of ρ (kg/m3), and that a pressure P (N/m2) is exerted on the upper surface of the column (Figure 2). The pressure P of the fluid at the base of the column-called the hydrostatic pressure of the fluid-is, by definition, the force F exerted on the base divided by the base area A. F thus equals the force on the top surface plus the weight of the fluid in the column. It is not difficult to show that:

P = Po + ρ g h

Example

Express a pressure of 200,000 Pa in terms of mmHg.

Example:

What is the pressure 30 m below the surface of a lake? Atmospheric pressue is 10.4 m H2O and the density of water is 1000 kg/m3.

3.4b Atmospheric Pressure, Absolute Pressure, and Gauge Pressure

A typical value of the atmospheric pressure at sea level, 760.0 mmHg, has been designated as a standard pressure of 1 atmosphere.

The fluid pressures referred to so far are all absolute pressures, in that a pressure of zero corresponds to a perfect vacuum. Many pressure-measuring devices give the gauge pressure of a fluid, or the pressure relative to atmospheric pressure. A gauge pressure of zero indicates that the absolute pressure of the fluid is equal to atmospheric pressure. The relationship for converting between absolute and gauge pressure is:

Pabsolute = Pgauge + Patmospheric

The abbreviations psia and psig are commonly used to denote absolute and gauge pres¬sure in lb/in.2. Also, it is common to refer to negative gauge pressures (absolute pressures less than atmospheric) as positive amounts of vacuum: for example, a gauge pressure of -1 cm Hg (75.0 cm Hg absolute if atmospheric pressure is 76.0 cm Hg) may also be called 1 cm of vacuum.

Fluid Pressure Measurement

Perry's Chemical Engineers' categorizes pressure-measurement devices as:

• elastic-element methods-Bourdon tubes, bellows, or diaphragms

• liquid-column methods-manometers

• electrical methods-strain gauges, piezoresistive transducers, and piezoelectric transducers

Bourdon gauge: The most common mechanical device used for pressure measurement, which is a hollow tube closed at one end and bent into a C configuration. The open end of the tube is exposed to the fluid whose pressure is to be measured. As the pressure increases, the tube tends to straighten, causing a pointer attached to the tube to rotate. The position of the pointer on a calibrated dial gives the gauge pressure of the fluid. Bourdon gauges are used to measure fluid pressures from nearly perfect vacuums to about 7000 atm.

Manometers: More accurate measurements of pressures below about 3 atm. A manometer is a U-shaped tube partially filled with a fluid of known density (the manome¬ter fluid). When the ends of the tube are exposed to different pressures, the field level drops in the high-pressure arm and rises in the low-pressure arm. The difference between the pressures can be calculated from the measured difference between the liquid levels in each arm.

Example Pressure Measurement with Manometers

1. A differential manometer is used to measure the drop in pressure between two points in a process line containing water. The specific gravity of the manometer fluid is 1.05. The measured levels in each arm are shown below. Calculate the pressure drop between points I and 2 in dynes/cm2.

2. The pressure of gas being pulled though a line by a vacuum pump is measured with an open¬ed mercury manometer. A reading of -2 in. is obtained. What is the gas gauge pressure in inches of mercury? What is the absolute pressure if Patm = 30 in. Hg?

3.4a Fluid Pressure and Hydrostatic Head

Pressure is the ratio of a force to the area. Accordingly, pressure units are force units divided by area units (e.g., N/m`, dynes/cm2, and lbf/in.2 or psi). The SI pressure unit, N/m2, is called a pascal (Pa).

Consider a fluid (gas or liquid) contained in a closed vessel or flowing through a pipe, and suppose that a hole of area A is made in the wall of the containing vessel, as in Figure 1. The fluid pressure may be defined as the ratio F/A, where F is the minimum force that would have to be exerted on a frictionless plug in the hole to keep the fluid from emerging.

Suppose a vertical column of fluid is h(m) high and has a uniform cross-sectional area A(m2). Further suppose that the fluid has a density of ρ (kg/m3), and that a pressure P (N/m2) is exerted on the upper surface of the column (Figure 2). The pressure P of the fluid at the base of the column-called the hydrostatic pressure of the fluid-is, by definition, the force F exerted on the base divided by the base area A. F thus equals the force on the top surface plus the weight of the fluid in the column. It is not difficult to show that:

P = Po + ρ g h

Example

Express a pressure of 200,000 Pa in terms of mmHg.

Example:

What is the pressure 30 m below the surface of a lake? Atmospheric pressue is 10.4 m H2O and the density of water is 1000 kg/m3.

3.4b Atmospheric Pressure, Absolute Pressure, and Gauge Pressure

A typical value of the atmospheric pressure at sea level, 760.0 mmHg, has been designated as a standard pressure of 1 atmosphere.

The fluid pressures referred to so far are all absolute pressures, in that a pressure of zero corresponds to a perfect vacuum. Many pressure-measuring devices give the gauge pressure of a fluid, or the pressure relative to atmospheric pressure. A gauge pressure of zero indicates that the absolute pressure of the fluid is equal to atmospheric pressure. The relationship for converting between absolute and gauge pressure is:

Pabsolute = Pgauge + Patmospheric

The abbreviations psia and psig are commonly used to denote absolute and gauge pres¬sure in lb/in.2. Also, it is common to refer to negative gauge pressures (absolute pressures less than atmospheric) as positive amounts of vacuum: for example, a gauge pressure of -1 cm Hg (75.0 cm Hg absolute if atmospheric pressure is 76.0 cm Hg) may also be called 1 cm of vacuum.

Fluid Pressure Measurement

Perry's Chemical Engineers' categorizes pressure-measurement devices as:

• elastic-element methods-Bourdon tubes, bellows, or diaphragms

• liquid-column methods-manometers

• electrical methods-strain gauges, piezoresistive transducers, and piezoelectric transducers

Bourdon gauge: The most common mechanical device used for pressure measurement, which is a hollow tube closed at one end and bent into a C configuration. The open end of the tube is exposed to the fluid whose pressure is to be measured. As the pressure increases, the tube tends to straighten, causing a pointer attached to the tube to rotate. The position of the pointer on a calibrated dial gives the gauge pressure of the fluid. Bourdon gauges are used to measure fluid pressures from nearly perfect vacuums to about 7000 atm.

Manometers: More accurate measurements of pressures below about 3 atm. A manometer is a U-shaped tube partially filled with a fluid of known density (the manome¬ter fluid). When the ends of the tube are exposed to different pressures, the field level drops in the high-pressure arm and rises in the low-pressure arm. The difference between the pressures can be calculated from the measured difference between the liquid levels in each arm.

Example Pressure Measurement with Manometers

1. A differential manometer is used to measure the drop in pressure between two points in a process line containing water. The specific gravity of the manometer fluid is 1.05. The measured levels in each arm are shown below. Calculate the pressure drop between points I and 2 in dynes/cm2.

2. The pressure of gas being pulled though a line by a vacuum pump is measured with an open¬ed mercury manometer. A reading of -2 in. is obtained. What is the gas gauge pressure in inches of mercury? What is the absolute pressure if Patm = 30 in. Hg?

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