Question

What gauge pressure is required in the city water mains for a stream from a fire hose connected to the mains to reach a vertical height of 15.0 m? (Assume that the mains have a much larger diameter than the fire hose.)

Why is your P2 equal to zero atm, when it is actually supposed to be 1atm since at this point in the water is exposed to air pressure. Is air pressure not 1atm?

Answer 1

Using Bernoulli's theorem at initial and final point

P1 + (1/2)*rho*V1^2 + rho*g*h1 = P2 + (1/2)*rho*V2^2 + rho*g*h2

V1 = speed of water in mains = 0 m/sec (since given that mains have a much larger diameter than the fire hose)

V2 = 0, since given that water reaches a vertical height, So this is max height, and at max height velocity becomes zero

h1 = 0 m, and h2 = 15.0 m, So

P1 + 0 + 0 = P2 + 0 + rho*g*h2

P1 = P2 + rho*g*h2

here P2 is not equal to 0 atm, it's equal to atmospheric pressure, So

P1 = P_atm + 1000*9.81*15.0

P1 = P_atm + 147150

Now since we need gauge pressure at water mains, So

P_gauge = absolute pressure - atmospheric pressure = P1 - P_atm

P_gauge = P_atm + 147150 - P_atm

P_gauge = 147150 Pa = 1.47*10^5 Pa

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