A pump circulates water through a system of connected pipes on a house from the basement...
A pump circulates water through a system of connected pipes on a house from the basement to the top floor. The pump is located in the basement and drives water at 3.93m/s through a 6.99 cm diameter pipe at a gauge pressure of 425000 Pa.
What will be the pressure (in kPa) in a 3.19 cm diameter pipe on the top floor, 21.6 m above the pipe? Please show work!
Homework Answers
Using continuity equation:
A1v1 = A2v2
v2 = A1v1/A2
A = pi*r^2 = pi*d^2/4
v2 = v1*(d1/d2)^2
v2 = 3.93*(6.99/3.19)^2 = 18.87 m/sec
Now using bernoullis' law:
P1 + 0.5*rho*v1^2 + rho*g*h1 = P2 + 0.5*rho*v2^2 + rho*g*h2
h1 - h2 = -21.6 m
P1 = 4.25*10^5 Pa
P2 = 4.25*10^5 + 0.5*1000*(3.93^2 - 18.87^2) - 1000*9.81*21.6
P2 = 42.79*10^3 Pa = 42.79 kPa
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