Chapter 2: Fluid PressureZaifah Bt. Che WilDepartment of Civil EngineeringPoliteknik Sultan Idris Shah

Jun 2014

UPON COMPLETING THIS CHAPTER, THE STUDENTS ARE EXPECTED TO BE ABLE TO

2.1 Understand pressure and pressure variation in a fluid at rest.

2.1.1Explain the concept of pressure and pressure head 2.1.2Explain the relationship between absolute pressure, gauge pressure, and atmospheric pressure. 2.1.3Describe the properties of air at standard atmospheric pressure. 2.1.4Explain the relationship between a change in elevation and the change in pressure in a fluid. 2.1.5Describe a barometer, piezometer, U-tube manometer. 2.1.6Determine the pressure difference in manometer

PressurePressure is defined as a normal force exerted by a fluid per unit area.Units of pressure are N/m2, which is called a pascal (Pa). Since the unit Pa is too small for pressures encountered in practice, kilopascal (1 kPa = 103 Pa) and megapascal (1 MPa = 106 Pa) are commonly used.Other units include bar, atm, kgf/cm2, lbf/in2=psi.

Absolute, gage, and vacuum pressuresActual pressure at a give point is called the absolute pressure.Most pressure-measuring devices are calibrated to read zero in the atmosphere, and therefore indicate gage pressure, Pgage=Pabs - Patm.Pressure below atmospheric pressure are called vacuum pressure, Pvac=Patm - Pabs.

Absolute, gage, and vacuum pressures

Pressure at a PointPressure at any point in a fluid is the same in all directions.Pressure has a magnitude, but not a specific direction, and thus it is a scalar quantity.

Scuba Diving and Hydrostatic Pressure

Pressure on diver at 100 ft?

Scuba Diving and Hydrostatic Pressure100 ft12

Variation of Pressure with DepthIn the presence of a gravitational field, pressure increases with depth because more fluid rests on deeper layers.

Measurement of PressureBarometerPiezometerManometerDifferential ManometerU-tube Differential ManometerInverted U-tube Differential Manometer

The BarometerAtmospheric pressure is measured by a device called a barometer; thus, atmospheric pressure is often referred to as the barometric pressure.PC can be taken to be zero since there is only Hg vapor above point C, and it is very low relative to Patm. Change in atmospheric pressure due to elevation has many effects: Cooking, nose bleeds, engine performance, aircraft performance.

The PiezometerSimplest form of pressure measuring device.The pressure at A is equal to the pressure due to the column of liquid of height h

The ManometerA device based on this is called a manometer.A manometer consists of a U-tube containing one or more fluids such as mercury, water, alcohol, or oil.Used to measure pressure difference between two pointsManometers use the relationship between pressure and head to measure pressure

Example 1

The right limb of a simple U-tube manometer containing mercury is open to the atmosphere while the left is connected to a pipe in which a fluid of sp. gr. 0.9 is flowing. The centre of the pipe is 12 cm below the level of mercury in the right limb. Find the pressure of fluid in the pipe if the difference of mercury level in the two limbs is 20 cm.

Example 2

A simple U-tube manometer containing mercury is connected to a pipe in which a fluid sp. gr. 0.8 and having vacuum pressure is flowing. The other end of the manometer is open to atmosphere. Find the vacuum pressure in pipe, if the difference of mercury level in the two limbs is 40 cm and the height of fluid in the left from the centre of pipe is 15 cm below.

U-tube differential manometerU-Tube enables the pressure of both liquids and gases to be measuredU is connected as shown and filled with manometric fluid.Important points: The manometric fluid density should be greater than of the fluid measured.The two fluids should not be able to mix they must be immiscible.Two pipes at different level A and B at the same level

Example 3

A differential manometer, when connected to two pipes A and B, gives the readings as shown in Figure 2.7. Determine the pressure (kN/m2) in the tube A, if the pressure in the pipe B be 55 kN/m2.

SolutionGiven; PB = 55 kN/m2 = 55 x 103 N/m2

Example 4A differential manometer is connected at two points A and B of two pipes as shown in Figure 2.8. The pipe A contains a liquid of sp. gr. = 1.5 while pipe B contains a liquid of sp. gr. = 0.9. The pressure at A and B are 98.1 kN/m2 and 176.58 kN/m2 respectively. Find the difference in mercury level in the differential manometer.

Inverted U-tube differential manometer

Consist of an inverter U-tubeContaining a light liquidUsed for measuring difference of low pressure

Example 5In below Figure 2.10 shows an inverted differential manometer connected to two pipes A and B containing water. Find the differential of pressure between pipes A and B.

Exercise 1Determine the pressure of A if given h= 0.3 and h1=0.6m. Where the fluid in pipe is water(sp.gr = 0.8) and the fluid in manometer is mercury (sp.gr = 13.6)

ans PA = 114.188kN/m2*