The pump shown in the figure supplies energy to the flow such that the upstream
ID: 1829003 • Letter: T
Question
The pump shown in the figure supplies energy to the flow such that the upstream pressure {12 in. pipe) is 5 psi and the downstream pressure (6 in. pipe) is 55 psi when the flow of water is 3.0 cfs. What horsepower is delivered by the pump to the flow? Assume a. = 1.0 at all locations.
The pump shown in the figure supplies energy to the flow such that the upstream pressure {12 in. pipe) is 5 psi and the downstream pressure (6 in. pipe) is 55 psi when the flow of water is 3.0 cfs. What horsepower is delivered by the pump to the flow? Assume a. = 1.0 at all locations.Explanation / Answer
Using Bernoullis equation at inlet and exit point for pump
W + P1/R*g + Z + 0.5*m*V1^2/R*g = P2/R*g + Z + 0.5*m*V2^2/R*g
Where Z is height, as both pipes are at same level, the term gets cancelled
R is density of fluid here R=1000 kg/m3
V1 and V2 are velocities at 1 & 2
W is power required in f ie pressure head.
g = 9.81 m/s2
V1 = flow / area of pipe
flow = 4.91 x 10(-5) m3/s
radius = 6 in = 0.1524 m
V1= 4.91 x 10(-5)/( pi*0.1542*0.1542) = 6.54e-4
V2= 4.91 x 10(-5)/ (pi*0.0762*0.0762)=2.69e-3
Also mass flow rate = flow* density = 4.91e(-5)*1000 = 4.91e(-2) /sec
P1=34473.75 Pa
P2=379211.25 Pa
W=3.514 m
In power terms Pow = W* density*acceleration
Pow = 3.514*9.81*1000 =34473.75 Watts
Power=46.2 HP
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