CHAPTER 4
FLUID-FLOW APPLICATIONS (cont'd)

SUMMARY

1. Pressure in fluids can be measured by instruments such as the piezometer tube, the U-tube and the Bourdon tube.

2. Velocity can be measured by instruments such as the Pitot tubes - static tubes where:

  v² = 2gZ

and Venturi meters where:

v² = [2(P₂ -P₁)/r] x A₂²/(A₂² -A₁²)
      = 2(P₂ -P₁)A₂²/r(A₂² -A₁²)

3. Basic pumps for liquids include reciprocating, gear, vane and centrifugal types.
Fans for air and gases are usually either centrifugal or axial flow (propeller) types.

1. The difference in levels between a fluid in the two legs of a U-tube is 4.3 cm. What differential pressure is there between the surfaces of the fluid in the two legs if the fluid in the tube is (a) water, (b) soyabean oil and (c) mercury?
[(a) 0.42 kPa; (b) 0.38 kPa; (c) 5.74 kPa

2. A Pitot tube is to be used for measurement of the rate of flow of steam at a pressure of 300 kPa above atmospheric pressure, flowing in a 10 cm diameter pipe. If it is desired to measure flow rates in this pipe of between 300 and 600 kg h^-1, what would be the differential pressures across the tube, in mm of water?
[ for 300 kg h^-1, 3.48 mm water; for 600 kg h^-1, 13.9 mm water ]

3. If across a 2 cm diameter orifice measuring the flow of brine of density 1080 kg m^-3 in a 5 cm diameter pipe, the differential pressure is 182 Pa, estimate the mass rate of flow of the brine. Take the orifice discharge coefficient as 0.97.
[ 695 kg h^-1]

4. A Venturi meter is being used to determine the flow of soyabean oil at 65°C in a pipe. The particular pipe is 15 cm in diameter, which decreases to 6 cm in the throat of the Venturi. If the differential pressure is measured as 14 cm of water, estimate the flow rate of the soyabean oil.
[ Volume 0.17 m³ h^-1; Mass 153 kg h^-1 ]

5. A volume of 0.5 m³ h^-1 of water is being pumped at a velocity of 1.1 m s^-1 from the bottom of a header tank, 3 m deep, down three floors (a total fall of 10 m from the bottom of the header tank) into the top of a water pressure tank which is maintained at a pressure of 600 kPa above atmospheric. Estimate the theoretical pump power required, ignoring pipe friction.
[ 0.09 HP ]

6. In the pumping system of worked Example 4.3, the actual pump selected for the duty would pump more water than the 1.2 m³ min^-1 needed for the duty. By plotting a capacity curve for the system, varying the flow rate and determining the total head for each selected rate, determine from the interaction of this curve and the pump characteristic curve, the expected flow rate. Assume flow is turbulent.
[ Flow rate = 1.62 m³ min^-1]

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