Basic Mechanical Engineering (3110006)

BE | Semester-1   Summer-2019 | 04-06-2023

Q3) (c)

A double acting reciprocating pump has piston diameter of 150 mm and stroke length of 225 mm. the suction and delivery heads are 4 m and 12 m respectively. If the speed of the pump is 80 rpm and the actual quantity of water discharged is 0.61  m3min. find the percentage slip, the coefficient of discharge and the power required to drive the pump if the efficiency of the pump is 80 %.

Given Data:
D = 150 mm = 0.15 m
L = 225 mm = 0.225 m
hs = 4 m
hd = 12 m
N = 80 rpm
Qact = 0.61 m3min = 0.0101 m3s
η = 80%
 
Find:
1) % Slip
2) Cd
3) P
 
Solution:
1) % Slip
 
Qth =  2 × A × L × N 60 =   π 4× 0.152 × 0.225 × 80 60 = 0.0106  m3s
 
% Slip =  Qth - Qact Qth × 100 %=  0.0106 - 0.0101 0.0106  × 100 % = 0.049
 
2) Cd
 
Cd =  Qact Qth =  0.0101 0.0106  = 0.95
 
3) P
 
P =  2 × ρg × A × L × N × hs + hdQth
 
P =  2 × 100 × 9.81 ×  π4 × 0.152 × 0.225 × 80 × 4 + 12Qth
 
P  = 1.66 kW
 
Actual power required is,
 
Pact =  P Cd =  1.66 0.95  = 2.075 kW