Hello, I'm new here - so apologies in advance if this is in the wrong place, also I haven't done physics for a few years prior to the course I just started - and I've never tried to write out formula in computer text, so apologies in advance again if everything I write is completely wrong! :tongue2:(adsbygoogle = window.adsbygoogle || []).push({});

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

A Farmer builds a water storage tank12mabove ground, as shown below:

[PLAIN]http://img408.imageshack.us/img408/6195/irrigationsystem.jpg [Broken]

The water is fed via a200mlong,125mmdiameter pipe to a field for irrigation purposes. The pipe has a friction factor of0.008. Using the K data below, show that thewater flow rate(kg/s) in the pipe is approximately26kg/s

Data:

K Factors:Tank Exit 0.5, Bends 0.9 (x2), Valve 1.0 (Total: 3.3)

Water Density: 1000kg/m3

2. Relevant equations

Bernoulli's Equation:(P_1/ρ*g) + (V_1^/2*g) + z1 = (P_2/ρ*g) + (V_2^/2*g) + z2

Darcy Formula:H_f = 4*f*(L/D)*(V^/2*g)

Moody Diagram

3. The attempt at a solution

Right then, I've been asked to find the water flow rate, which I'm presuming means themass flow rate(kg/s) - so in order to find that I need thevolume flow rate, and in order to find that I need thevelocity

I haven't been given thevelocityin the original problem, however I think I need to use theBernoulli Equationin order to find thevelocity.

I've made a few assumptions with the Bernoulli Equation, which are that thepressure at point 1(the water tank) is atmospheric (101325pa) - because on the picture the tank looks to be open to atmosphere, I've also assumed that thepressure at point 2(the end of the pipe) is also atmospheric (101325pa) because the pipe is leading to a field.

As well as this I've assumed that thevelocity at point 1is approximately0m/s(because the water is going from a large tank into a small pipe)

So at the moment, myBernoulli equationlooks like:

(101325 / (1000 x 9.81)) + (0^ / (2 x 9.81)) + 12 = (101325 / (1000 x 9.81)) + (V_2^ / (2 x 9.81)) + 0

However I understand that this equation isn't full, as I also have to take into account thefriction (head loss), which would change theBernoulli equationinto:

(P_1/ρ*g) + (V_1^/2*g) + z1 = (P_2/ρ*g) + (V_2^/2*g) + z2 + h_f

So in order to accurately find thevelocityusing theBernoulli equation, I have to also take into account theHead loss?

But theDarcy Formulais:H_f = 4*f*(L/D)*(V^/2*g)

So in order to use theDarcy FormulaI have to know thevelocity- but I don't know thevelocity(as that's what I'm trying to find)? - Unless there's a way of finding thehead losswithout knowing thevelocity?

Which somewhat puts me at a dead end.

Another route I was thinking of using to find thevelocitywas to use theMoody Diagramto try to find theReynolds number, then usingRe=(ρ*V*D)/μto find thevelocity(as I know all the other values.)

However the only otherMoody diagramvalue I know is theFriction Factorof0.008, and I'm unable to find theRelative roughness(k/D) as the problem doesn't state what sort of pipe is being used (so I can't find the roughness.)

You can probably tell by now that I'm completely stumped by this - and as far as I know I'm probably doing it all completely wrong (it seems no matter what I try to do I always end up with a missing variable), so any help would be very much appreciated.

(Updated to include picture.)

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# Homework Help: Fluid flow rate and friction problem

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