CENG 231 Process Fluid Mechanics
Tutorial Examples 3

1. Oil of relative density 0.85 issues from a 50 mm diameter orifice under a pressure of 100 kPa (gauge). The diameter of the vena contracta is 39.5 mm and the discharge is 18 litres / s. What is the coefficient of velocity?

(Ans. :0.958 )

2. A sharp­edged orifice, 5 cm in diameter, in the vertical side of a large tank discharges under a head of 5 m. If Cc = 0.62 and Cv = 0.98, determine a) the diameter of the jet at the vena contracta, b) the velocity of the jet at the vena contracta and c) the discharge in cubic meters per second.

(Ans.: a) 3.94cm, b)9.71 m/s, c)0.0118m3/s)

3. Find the diameter of a circular orifice to discharge 0.015 m3 / s under a head of 2.4 m using a coefficient of discharge of 0.6. If the orifice is in a vertical plane and the jet falls 0.25 m in a horizontal distance of 1.3 m from the vena contracta, find the value of the coefficient of contraction.

(Ans.: 6.82 cm, 0.716 )

4. Consider a large, vertical, rectangular orifice of breadth b and depth d discharging fluid into the atmosphere. Show that

What happen if H >> d?

5. A pilot­static tube is used to measure air velocity. If a manometer connected to the instrument indicates a difference in pressure head between the tappings of 4 mm of water, calculate the air velocity assuming the coefficient of the pitot tube to be unity. Density of air is 1.2 kg / m3.

(Ans.: 8.08 m/ s)

6. Show that if a pilot­static tube immersed in a stream of fluid of density p,, is connected to a U­tube manometer containing a manometric fluid of density p2, the velocity of fluid flowing immediately upstream of the pilot­static tube is given by

where h is the manometric reading and k is a calibration constant.

7. A pilot­static tube is located in the center of an air duct to measure the velocity on the duct axis. An inclined manometer containing fluid of relative density 0.785 is connected to the pilot­static tube to measure the pressure difference between the tappings. If the inclined tube of the manometer makes an angle of 15o with the horizontal and the ratio of the diameters of the enlarged vertical tube to the inclined tube is 5, find the decrease in velocity in the duct if the manometer deflection along the inclined tube decreases from 150 mm to 100 mm.

(Ans. :4.4m/s)

8. A vertical venturi meter carries a liquid of relative density 0.8 and has inlet and throat diameters of 150 mm and 75 mm respectively. The pressure connection at the throat is 150 mm above that at the inlet. If the actual rate of flow is 40 litres / s and the coefficient of discharge is 0.96, calculate a) the pressure difference between inlet and throat, and b) the difference of levels in a vertical U­tube manometer connected between these points, the tubes above the mercury being full of liquid. (Relative density of mercury is 13.56.)

(Ans.: a) 34.53 kPa, b) 266.45 mm )

9. The throat and full bore diameters of a venturi meter are 19 mm and 57 mm respectively. Calculate the coefficient of discharge of the meter if the pressure at the full bore section is 172.5 kPa above that at the throat when the meter is passing 311 dm3 / min. of water. The centerline of the meter is inclined to the horizontal, the throat section being 0.46 m above the full bore section.

(Ans.: 0.991 )

10. A venturi meter in a horizontal 300 mm diameter water pipe has a throat diameter of 100 mm and a discharge coefficient of 0.98. A mercury U­tube was used to measure the difference of head between the pipe inlet and the throat at points 0.6 m apart. If the mercury gauge reading was 760 mm, find the flow through the pipe in dm3 / s. The connections to the U­tube are filled with water.

If the meter had been placed vertically with the flow upward, what would have been the gauge reading for the same rate of flow?

The relative density of mercury is 13.56.

(Ans.: 106 dm3 / s, 807.77 mm )

11. Derive an expression for the rate of flow through an inclined venturi meter and show that, if a U­tube type of gauge is used to measure the pressure difference, the gauge reading will be the same for a given discharge irrespective of the inclination of the meter.

A vertical venturi meter measures the flow of oil of specific gravity 0.82 and has an entrance of 125 mm diameter and a throat of 50 mm diameter. There are pressure gauges at the entrance and at the throat, which is 300 mm above the entrance. If the coefficient for the meter is 0.97, find the flow in m3 / s when the pressure difference is 27.5 kPa.

(Ans. :0.0151 m3/s)