# Fluid Dynamics in Pipe Lines Problem

1. Jul 11, 2016

### Elien

Hello!
Please help me understand whether I'm going to the right direction with the solution or partially wrong or completely wrong. I have a basic Fluid Mechanics course at the uni, the following problem is from a past exam my teacher gave us to practice before the exam, so there're no answers and I can't know if my solution is correct or not.
I just want you to say at least whether my solution is close to the truth or there're just some errors or I've solved it completely wrong. But if you can provide corrections to errors (if any), I'd be really grateful to you! Thank you in advance for your time!

P.S. There might be some improper English used in the problem statement or in my explanations since I'm not a native speaker and the teacher said that he translated the problems himself from German (he's German but running this course in English).

1. The problem statement, all variables and given/known data

A pressure drop of 15000 Pa is measured in a 10 m long water pipe with an inner diameter of di = 100 mm. Calculate the friction loss coefficient f if the flow rate in the pipe is 50 l/min.
Take the density of water equal to 1000 kg/m3 and the kinematic viscosity μ = 10-6 m2/s.

2. Relevant equations
1. I suppose that we should use here continuity equation (V/t = w*A) first for finding the flow velosity.
2. And then the Darcy equation (Δp = λ (L / di) (ρ*w2 / 2)) for calculation of friction factor (do I understand right that "the friction loss coefficient f" from the question is the same as friction factor lambda λ? At the lesson we only used lambda as a denotion for a friction factor or friction coefficient, so I just assumed that f and λ are the same, are they?

3. The attempt at a solution
1. First using the equation of continuity I solved for the flow velocity w, preceded by calculation of the area A of the water pipe and conversion of the flow rate from l/min to m3/s:
A = pi / 4 * di2 = pi / 4 * (0.1m)2 = 7.85 * 10-3 m2

V/t = 50 l/min = 50*0.001 m3 / 60 s = 8.3 * 10-4 m3/s

w = V/t / A = 8.3 * 10-4 m3/s / 7.85 * 10-3 m2 = 0.106 m/s

2. Now we can use the Darcy equation to solve for the friction coefficient f :

Δp = f (L / di) (ρ*w2 / 2)

f = Δp*di*2 / L*ρ*w2 = 15000*0.1*2 / 10*1000*(0.106)2 = 26.7

So according to my solution the answer should be f = 26.7, but I really doubt that it's correct, since 26.7 seems to me too big, and more than that I don't understand what for we are given the kinematic viscosity, should I also compute the Reynolds number, but also what for the Re then?