# Volume Flow Rate in a Pipe for Viscous Fluid

## Homework Statement

Hi, my first post here! I have a Thermodynamics resit over the summer and I'm trying to get my head around viscous flow, I'm stuck at a question and need help! Thanks :)

Glycerine discharges to the atmosphere through a circular pipe 100mm in diameter. The gauge pressure 50m from the exit is 458 kPa. Data for glycerine: ρ=1260 kg/m^3, μ=0.9 kg/ms.

Determine the volume flow rate Q for the following cases:
(i) a horizontal pipe (verify the flow is laminar!) (Ans: 25 litres/s)
(ii) a pipe inclined upwards by 20° (Ans: 13.5 litres/s)
(iii) a pipe inclined downwards by 20° (Ans: 36.5 litres/s)

## Homework Equations

I thought this equation was the right one to use but my answer is totally wrong when I plug the numbers in, it's not a units thing either...

Q = (∏d^4 / 128μ) * (ΔPloss / length)

## The Attempt at a Solution

I assumed the gauge pressure at the pipe exit is equal to atm pressure, so 100kPa - is this correct? The rest is just plugging numbers in. Am I missing something obvious here...?