Question

The water supply of a building is fed through a main pipe 7.00 cm in diameter. A 2.00 cm diameter faucet tap, located 2.10 m above the main pipe, is observed to fill a 25.0 L container in 30.0 s.

(a) What is the speed at which the water leaves the faucet?

correct answer of 2.65m/s

(b) What is the gauge pressure in the 7.00 cm main pipe? (Assume the faucet is the only "leak" in the building.)

Answer 1

Vol rate = 25 L/30 s = 0.0008333 (etc.) m^3/s
A1 = pi*0.03^2
A2 = pi*0.01^2
rho = 1000 kg/m^3
h2-h1 = 2.10 m
v1 = volrate/A1 = 0.073682844024023 m/s
v2 = volrate/A2 = 0.663145596216203 m/s (ans. A)
P2-P1 = -rho(g(h2-h1)+(v2^2-v1^2)/2) = -20579.78 Pa
P2 = 0, so P1 = 20579.7 Pa (ans. B)
There's one little thing. The flow rate parameter k affects the equations; it multiplies the velocity^2 term. For nonviscous flow (and uniform cross-section distribution of flow speed), k = 1; for viscous flow k = 4/3. I assumed k = 1; if you use 4/3, P1 changes to 20579.7 Pa.