The main water line enters a house on the first floor. The line has a gauge pressure of 1.94 x 105 Pa. (a) A faucet on the second floor, 4.90 m above the first floor, is turned off. What is the gauge pressure at this faucet? (b) How high could a faucet be before no water would flow from it, even if the faucet were open?

Answer

given,

gauge pressure = 1.94 x 10⁵ Pa

Pressure due to 4.90 m column of water

= ρ g h

= (4.90) x (1000) x (9.8) Pa

= 48020 Pa

Gauge pressure of second floor faucet

= 1.94 x 10⁵Pa - 48020 Pa

P_g = 145980 Pa

(b)

Let h = height of faucet from which no water can flow even if open

P = ρ g h

1.94 x 10⁵ = h x (1000) x (9.8)

h = 19.79 m