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CBB 1033 Chem. Eng. Fluid Mechanics
January 2011
Tutorial 3 Chapter 3: Conservation of energy 1.
The jet of water is initially 12 cm in diameter and when directed vertically upwards reaches a maximum height of 20 m. Assuming that the jet remains circular determine the rate of water 3 flowing and the diameter of the jet at a height of 10 m. [0.224 m /s, 14.27 cm]
Solution:
2.
A pipe AB carries water and tapers uniformly from a diameter of 1 m at A to 0.2 m at B over a length of 2 m. Pressure gauges are installed at A, B and also at C, the midpoint of AB. If the pipe o centerline slopes upwards from A to B at an angle of 30 and the pressures recorded at A and B are 2.0 and 2.3 bar, respectively, determine the flow through the pipe and pressure recorded at C 3 neglecting all losses. [0.0723 m /s, 2.29 bar]
1
CBB 1033 Chem. Eng. Fluid Mechanics
January 2011
2
CBB 1033 Chem. Eng. Fluid Mechanics
January 2011
3.
A venturi meter with a throat diameter of 100 mm is fitted in a vertical pipeline of 200 mm 3 diameter with oil of specific gravity 0.88 flowing upwards at a rate of 0.06 m /s. The venturi meter coefficient is 0.96. Two pressure gauges calibrated in kPa are fitted at tapping points, one at the throat and the other in the inlet pipe 320 mm below the throat. The difference between the two gauge pressure readings is 28 kPa. Working from Bernoulli’s equation, determine the difference in level in the two limbs of a mercury manometer if it is connected to the tapping points and the connecting pipes are filled with the same oil. [202 mm]
4.
An orifice plate is to be used to measure the rate of air flow through a 2 m diameter duct. The mean velocity in the duct will not exceed 15 m/s and a water tube manometer, having a maximum difference between water levels of 150 mm, is to be used. Assuming coefficient of discharge to be 0.64, determine a suitable orifice diameter to make full use of the manometer range. Take the density of air as 1.2 kg/s.
[1.31 m]
3
CBB 1033 Chem. Eng. Fluid Mechanics
5.
January 2011
A venturi meter is constructed from a pipe with a diameter of 300 mm. The venturi has a throat diameter of 100 mm and a discharge coefficient of 0.98. A mercury U-tube was used to measure the difference of head between the pipe inlet and the throat at points 0.6 m apart. The connections to the U-tube are filled with water. If the mercury gage reading was 760 mm, find the volumetric flow rate through the pipe. (116.2 L/s)
Solution: 1
2 P P 2 1 A A 2
A closed tank partially filled with water discharges through an orifice of 12.5 mm diameter and has a coefficient of discharge of 0.7. If air is pumped into the upper part of the tank, determine the 3 pressure required to produce a discharge of 36 dm /min when the water surface is 0.9 m above the outlet. (15.7 kPa)
Solution: z1 = 0, V 1 = 0
z2 = – 0.9 m dnozzle = 0.0125 m P2 = Patm = 0 kpa gage Cd = 0.7 -4 3 -4 3 Qactual = 6 10 m /s Qideal = 8.57 10 m /s
V2
8.57 10
4
4
7
m s
0.0125
2
Assumption: Water flows out steadily, frictionless nozzle, no work interaction P2 P1
P1
2
g z2 z1
9.81 0.9
2
V2 V1 2
0
0 P1
2
0.9 0 9.81
7 0 2
0
49 2
P1 15.67 kPa
7.
A siphon has a uniform circular bore of 75 mm diameter and consist of a bent pipe with its crest 1.8 m above water level discharging into the atmosphere at a level 3.6 m below water level. If the atmospheric pressure is equivalent of 10 m of water, determine: a. The outlet velocity (8.4 m/s) 3 b. The flow rate out (0.0371 m /s, 37.1 kg/s) c. The absolute pressure at crest level. Neglect the losses due to friction.
(45.1 kPa)
5
CBB 1033 Chem. Eng. Fluid Mechanics
January 2011
Solution: 2
1.8 m 1
3.6 m
3 Assumption: No work interaction, friction loss is negligible, tank is large that V 1 0 a.
