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I've frequented this forum for various purposes and this is the first time I've decided to post! Hopefully I can find the help or conformation I'm looking for. I may not have all the necessary info, but I feel this is basic enough that I should be able to come up with an appropriate answer.

This is a basic setup where I have water being pumped through steel piping and I'm trying to find the exit pressure and velocity of the water. Here is what I know for sure.

Pipe Diameter, d = .151in or .003835m

Pipe Length, l = 72in or 1.8288m

Pressure from pump, P = 100psi or 689400Pa

Temp, T = 140°F or 60°C

Density, ρ = 983.2 kg/m³

Viscosity, μ = 0.467*10-³ N*s/m²

Roughness steel, ε = .000025 m

Now somewhere in here I feel I am going about this wrong, so please bear with me.

1. To get the velocity of the water at the starting point I use Bernoulli's equation for dynamic pressure, q=1/2*ρ*v². Solving for v, I get v=37.45 m/s.

2. I calculate my Reynolds Number and relative roughness of the steel pipe, then use the Moody chart to determine the Friction Factor.

Re = (ρ*v*d)/μ = (983.2*37.45*.003835)/(.467*10-³) = 301,978

RR = ε/d = (.000025)/(.003835) = .00652

From the Moody chart: f = .031

3. Calculating the pressure drop due to the friction in the pipe (I feel this is my problem)

ΔP= (ρ*v²*f*l)/(2*d) = (983.2*37.45²*.031*1.8288)/(2*.003835) = 10192437.5 Pa

From there I would use Bernoulli's equation for the flow at the beginning of the pipe, P + 1/2*ρ*v² + ρ*g*h (last part is negligible for me), set equal to an equation for the exit flow which incorporates the friction.

I feel as though I am making an incorrect assumption (or 2 or 3...) which is leading to such a large drop in pressure. Areas I feel I could have gone astray; calculating the initial velocity using the dynamic pressure equation, assuming that friction will even have an effect here, or even that the pressure of the pump is way too high for such a small diameter pipe (and my calculations are somewhat correct).

If there is anyone out there that can comment on this and perhaps guide me in the right direction I'd greatly appreciate it.

Cheers and thanks for reading!

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# Fluid mechanics of water in a pipe

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