Flow Rate

The short answer is "depends". Based on the information given it could be anywhere from zero to free discharge. Ignoring losses, I believe you want the Bernoulli Equation. It will allow you to calculate the free discharge condition. The general form:

dP/rho + (v2²-v1²)/2 + g * dy = 0

where:

dP = change in pressure

rho = fluid density

v2 = final velocity

v1 = initial velocity

g = acceleration due to gravity

dy = change in height

Standardize your units and apply accordingly. I'm assuming v1 is zero and you'll be solving for v2. Knowing v2 and your pipe diameter, you can solve for flow rate.

If what you're really looking for is full-pipe flow, let me know and I'll write that equation out. But beware, it's not particularly nice...

Thank you , lets open the actual problem: in the plant I am working, there is a supply water pipiline of 1" dia. having pressure of 7 bar. I need to have a flow rate of 10 liter/min and pressure of 2.5 bar for my valve stand, cooling system purpose and I don't know the existing flow rate. Without using Flow meter & Pressure control valve etc., how do I find ( calculate) the required values . Plant water supply pipeline of 1" having 7 bar pressure available when it runs, now I need to get a supply line of 2.5 bar & 10 Liter/min flow.

Okay, it's been forever since I've done this, but here goes:

Use this form:

V₁²/2 + P₁/rho = V₂²/2 + P₂/rho

Flow(Q) in = Flow out; 10L/min = 10.17 in³/s

Q=AV => V₁=10.17/0.864 (True ID of 1" Sch.40 pipe = 1.049" => A₁=0.864 in²) = 11.77 in/s

P₁=101.53 psi, P₂=36.26 psi, rho=0.03613 lb/in³(water)

Therefore: 11.77²/2 + 101.53/0.03613 = V₂²/2 + 36.26/0.0361 => V₂=61.25 in/s

A₂=10.17/61.25=0.167 in² => d₂=0.46" (3/8" Sch.40 has true ID of 0.493")

Now, for the bad news. This assumes you have the flow you specified. If for some reason your supply does not deliver the 10 L/min you mentioned, none of this works. Long story short, you'll probably need to install a flow regulator.

So what happens when the upstream pressure changes? Are you happy with a change in flow, or a change in pressure or both?

What does Aequam memento rebus in arduis servare mentem mean ?

Loosely - "keep your wits when things are tough". It has some more eloquent translations, but that's the blue-collar version. It reminds me not to be overwhelmed when problems start coming rapidly and to focus on facts and solutions, not preconceptions and unknowns. A problem is only a problem until it's solved.