National University of Singapore Bachelor of Technology ME2135E -Fluid -Fluid Mechanics Mechanics II
Tutorial Sheet 1 (Turbomachinery- pumps) (1) A centrifugal centrifugal pump impeller impeller for pumping pumping water has has inner blade blade tip radius r 1 = 0.1 m and outer blade tip radius r 2 = 0.175 m. The blade widths at entry and exit are b 1 = b2 = 0.045 m with correspond corresponding ing blade angles 1 = 30° and 2 = 20°. For a running speed of 1440 rev/min, determine the following: (a) the flowrate through the impeller, and (b) the theoretical torque required to drive the impeller. You may assume the design conditions of whirl-free ( ( 1 = 90°) and shock-free entry to the impeller. [0.246 m3/s; 547.6 Nm]
(2) A centrifugal centrifugal pump pump has an impeller impeller with with dimensions dimensions r 1 = 7.5 cm, r 2 = 15 cm, b1 = 5 cm, b2 = 3 cm, 1 = 2 = 30°. For a discharge of 55 lit/sec and shock-free entry to vanes, compute (a) the speed, (b) the head, (c) the torque, (d) the power, and (e) the static pressure rise across the impeller. You may neglect neglect losses and and assume assume whirl free entry. entry. [514.8 rev/min; 3.888 m; 38.914 Nm; 2.0978 kW; 27.849 kPa]
(3) An axial flow pump pump operates at 500 rev/min. rev/min. The outer outer diameter of the impeller is 750 mm and the hub diameter is 400 mm. At the mean blade radius, the inlet blade angle is 12° and the outer blade angle is 15°, both measured with respect to the plane of the impeller rotation. Sketch the corresponding velocity diagrams at inlet and outlet, and estimate the following: (a) the head generated by the pump. (b) the rate of flow through the pump. (c) the shaft shaft power consumed consumed by the pump. pump. Assume a hydraulic efficiency of 87% and an overall efficiency of 70%. Volumetric efficiency may be assumed to be 1.0. [4.15 m; 1.012 m3/s; 58.89 kW]
(4) A given pump rotates at a speed of 1000 rev/min at its duty point and generates a head of 12.2 m when pumping water at a rate of 0.0151 m3/s. Calculate the head generated by a similar pump of twice the size operating under dynamically-similar condition and discharging 0.0453 m3/s. Assume the effects of viscosity are negligible. Determine also the rotational speed of the larger pump. [6.86 m; 375 rev/min]
(5) A centrifugal pump running at 2950 rev/min gave the following results at peak efficiency when pumping water during a laboratory test: Effective head H
=
75 m of water.
Flowrate Q = 0.05 m3 / s. Overall efficiency = 76%. (a)
Calculate the specific speed of the pump in dimensionless terms based on rotational speed in rev/s.
(b)
A dynamically-similar pump is to operate at a corresponding point of its characteristics when delivering 0.45 m3/s of water against a total head of 117 m. Determine the rotational speed at which the pump should be run to meet the duty and the ratio of its impeller diameter to that of the model pump tested in the laboratory; stating any assumptions made. What will be the power consumed by the pump?
[0.077; 1375 rev/min; 2.68; 679 kW]
(6) The characteristics of a pump in terms of dimensionless coefficients may be approximated by CH = 8 – 2CQ – 210CQ2. Such a pump having an impeller diameter 0.4 m and running at 24.17 rev/s operates against a system characteristics represented by H = 20 + 300 Q22. Determine the flowrate delivered and the pump's operating head. What would be the flowrate through the system if two such pumps are connected: (a) in series, and (b) in parallel. Use m3/s for Q, m for H and rev/s for N. [0.217 m3/s; 34.12 m; 0.255 m3/s; 0.326 m3/s]
(7)
A centrifugal pump has the following characteristics: Q (m3/hr) H (m) (%)
0 17 0.0
23 16 49.5
46 13.5 61.0
69 10.5 63.5
92 6.6 53.0
115 2.0 10.0
The pump is used to pump water from a low reservoir to a high reservoir through a total length of 800 m of pipe 15 cm in diameter. The difference between the water levels in the reservoirs is 8 m. Neglecting all losses except pipe friction and assuming f = 0.016, find the rate of flow between the reservoirs and the power input to the pump. If the static suction lift is 2 m and a quarter of the a pipe length is on the suction side of the pump, find the NPSH given that the barometric pressure is 740 mm Hg and the vapour pressure of water at the prevailing temperature is 26 mm Hg. (You may assume the specific gravity of Hg is 13.55). [59.5 m3/hr; 3.037 kW; 6.721 m]
(8)
A 60 cm diameter impeller centrifugal pump has the following characteristics at 750 rev/min: Q (m3/min) H (m)
0 40.0
7 40.6
14 40.4
21 39.3
28 38.0
35 33.6
42 25.6
49 14.5
56 0
(%)
0
41
60
74
83
83
74
51
0
(a) If the system resistance is purely frictional and is 40 m at 42 m3/min, determine the pump's operating point and the power absorbed. (b) The pump is used to supply water from one reservoir to another, the difference in water levels being 13 m. The pipeline is 45 cm in diameter, 130 m long, f = 0.02 and contains 2 gate valves (k = 0.2) and 10 right-angle bends (k = 0.35). Determine the volume flowrate delivered by the pump and the power required to drive the pump. (c) If for the system in (b) a geometrically similar pump 50 cm in diameter is used instead, running at 900 rev/min, determine the volume flowrate and the power consumed. [37 m3/min; 231.6 kW; 43.5 m3/min; 232.9 kW; 32.5 m3/min; 165.8 kW]
