Calcualte water discharge of a pipeline at different heights

[escobar147]

A pipeline is 8 km long and is required to convey water from a reservoir, at 500 m
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

The Attempt at a Solution

U1 = 0 Since the resovoir is stationary,

p1 = ρgh p2 = ρgh

putting values into 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!

 

[nvn]

escobar147: What is the reservoir depth at the pipe inlet? And what is the reservoir depth (if any) at the pipe outlet? It currently appears you made a mistake in computing either pressure p1 or p2, or on both p1 and p2. Show how you computed p1 and p2, and why?