# Homework Help: Bernoulli equation with losses dilemma

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1. Aug 11, 2016

### williamcarter

1. The problem statement, all variables and given/known data
Hello,Could you please lend me a hand with this problem?I would really appreciate it.
Question:

KL=2*0.75(2 elbows) D=5*10^-2 m ;f=0.001(fanning friction factor)
Point 1 which is at the top of the liquid in the tank:
h1=23 m; u1=0m/s(neglected due to Area differences) P1=0 gauge(atmos press)

Point 2 which is at the mouthpiece of fountain:
h2=0m(datum); u2=? P2=0 gauge(atmos press)

2. Relevant equations
We know bernoulli for losses with fanning friction factor
P1/ro*g+h1+u1^2/2*g=P2/ro*g+h2+u2^2/2*g +delta hloss

where delta hloss=K*u^2/2g
where K=f*4*L/D+Ki
where Ki=sum of K in our case 2*0.75(2 elbows)
where f is fanning friction factor.

3. The attempt at a solution
P1/ro*g+h1+u1^2/2*g=P2/ro*g+h2+u2^2/2*g +delta hloss
As we made the assumption in first step.This can be rewritten as:
h1=delta h loss
=>h1=K*u^2/2*g
h1=(f*4*L/D+Ki)*u^2/2g
=>u=sqrt(h1*2g)/(f*4*L/D+Ki)
and substituting values in this formula gives u=10.05 m/s
However their answer is 9.0 m/s

I do not understand
1) why they did Ki=0.5+2*0.75, from where comes that "0.5"?
2)From where comes that "1+" in their sqrt formula
2)Why they picked L=20+10+2

Thank you in advance , much appreciated.

2. Aug 11, 2016

### Staff: Mentor

In my judgment, all three items that you cited are errors that they made.

3. Aug 11, 2016

### williamcarter

Thank you very much for your quick response.
I would be more than glad if you could let me know how was the correct approach.

4. Aug 11, 2016

### Staff: Mentor

The 0.5 should be a 1, and the 1 shouldn't be there. I was wrong about the L. The total length of tubing is 20 + 10 (horizontal) + 2 (vertical).

5. Aug 20, 2016

### williamcarter

Thank you, could you please tell me why we need to add 20+10+2.
Why is it needed to add 20+10+2? And why we can't take in consideration just the height?
Why is it needed to do like that?
I mean why we cannot put just the height ,20 m?or 25m?

Last edited: Aug 20, 2016
6. Aug 20, 2016

### Staff: Mentor

The total length of tubing is 32 meters. This is the length that experiences a frictional pressure drop.

7. Aug 20, 2016

### williamcarter

Ok I understood this, thank you.But how do you know that?

8. Aug 20, 2016

### Staff: Mentor

Waddya mean? How long is the tubing?

9. Aug 21, 2016

### williamcarter

How do you know that?How did you identified that?What was the criteria to get to that value?What was the mechanism behind it?

10. Aug 21, 2016

### Staff: Mentor

If fluid flows in one end of a pipe and comes out the other end, doesn't it have to travel through the entire length of pipe to get from one end to the other? Isn't there viscous wall friction over the entire length?

11. Aug 21, 2016

### williamcarter

Yes,it is, thank you, now is clear, much appreciated.