Question

25 10 points Problem 4A Water at a gauge pressure of 3.8 atm at street level flows into an office building at a speed of 0.55 m/s through a pipe 4.5 cm in diameter. The pipe tapers down to 2.75 cm in diameter by the top floor, 18 m above, where the faucet has been left open. Calculate the velocity at the top of the floor. Give your answer in m/s to two decimal places. Do not type the units in the box, just the numerical value. Type your answer... 26 10 points Problem 4B Water at a gauge pressure of 3.8 atm at street level flows into an office building at a speed of 55 ms through a pipe 45 cm in diameter. The pipe tapers down to 2.75 cm in diameter by the top floor, 18 m above, where the faucet has been left open. Calculate the gauge pressure at the top floor you will need to use your answer from parta). Give your answer in Pato two decimal places. Do not type the units in the box just the numerical value. Type your answer

Answer 1

4A. given, water at gauge pressure Pg = 3.8 atm
at street level
flows into office building, speed, u = 0.55 m/s
dia of pipe is d = 4.5 cm

at the top floor,
dia of pipe is d' = 2.75 cm
heigth, h = 18 m

now, fron continuity equation
u*pi*d^2 = v*pi*d'^2 [ where v is speed of water at the top of the building]
hence
v = 0.55(4.5/2.75)^2
v = 1.472727272727 m/s

4B. let the gauge pressure at the top floor be P
then
from bernoullis theorem
Pg + 0.5*rho*u^2 = P + 0.5*rho*v^2 + rho*g*h
P = 3.8*1.01*10^5 + 0.5*1000*(0.55^2 - 1.472^2) - 1000*9.81*18
P = 2.062867*10^5 Pa = 2.042443 atm
P = 2.062867*10^5 Pa