Question

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!

Answer 1

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