Calculating pump pressure for 3000 lts/h flow through 1.25" pipe

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AdamTassle
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Hi all,

This is probably nauseatingly simple but I'm struggling to get my head round it and would very much appreciate assistance!

I'm building a filter system for a rather ambitious desert pool project and I'm having difficulty predicting the pressure in the pump/pipe network. I've been trawling the internet for a few hours but remain thoroughly confused.

I am trying to work out the necessary pump pressure (psi) to create a flow rate of 3000lts/h through a pipe of 1.25" diameter. I'm no great mathematician but I've been playing with Bernoulli's equation, unfortunately I only seem to be able to calculate pressure change, rather than pressure based on flow rate and constriction.

I have a feeling I am making a conceptual error of epic proportions! Would someone be kind enough to point out where I'm going wrong?

Thanks!
AT
 
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Flow in a pipe is dominated by viscous effects, and bernoulli won't help you very much here. Flow rate will depend on both the length and diameter of the pipe, and can actually be somewhat complex to determine (depending on the details).
 
Friction is the key. Use a pipe sizing chart and it'll tell you the frictional pressure drop for a given length of pipe: http://www.conergy.us/PortalData/3/Resources/products/solar_pumps/pdf/Pipe_Sizing_Chart.pdf

You'll also need the pressure drop across any fittings or devices in the pipe. And you're also going about the issue backwards, picking the pipe size before you know the associated pressure drop.
 
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If your pipe has elevation changes or changes in diameter, you do need to use Bernoulli. Engineers use the Bernoulli equation with an additional 'head loss' term to account for friction and the pressure drops in fittings or devices in the pipe.