A pipeline is 8 km long and is required to convey water from a reservoir, at 500 m(adsbygoogle = window.adsbygoogle || []).push({});

above datum, to the intake of a water treatment works at 425 m above datum. If

the pipe has a diameter of 225 mm, what is the discharge of water through the

pipe? The density of water is 1000 kg/m3.

relevant equations:

bernoullis Energy Conservation:

P1/ρg + u1^2/2g + z1 = p2/ρg + u2^2/2g + z2

mass conservation equation:

U1A1 = U2A2

Q1 = Q2

3. The attempt at a solution

U1 = 0 Since the resovoir is stationary,

p1 = ρgh p2 = ρgh

putting values in to bernoullis:

4905000/9810 + 500 = 4169250/9810 + u2^2/19.62 + 425

150 = u2^2/19.62

u2^2 = 2943

√2943 = 54.24 m/s

at this point the answer should be: 38.36 m/s

and the final answer should be: Q = 1.525m^3/s

i am completely lost, any help would be massively appreciated!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Calcualte water discharge of a pipeline at different heights

**Physics Forums | Science Articles, Homework Help, Discussion**