# Homework Help: Water flow in pipe with two open vertical offshoots

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1. Oct 29, 2014

### rlc

1. The problem statement, all variables and given/known data
Water (η = 1.00E-3 Pa·s) is flowing through a horizontal pipe with a volume flow rate of 0.0125 m3/s. As the drawing below shows, there are two vertical tubes that project from the pipe. Assume that H = 0.0458 m and L = 0.738 m.

Calculate the radius of the horizontal pipe.

3. The attempt at a solution
I've seen this problem posted on this website before, but the solution there didn't work for me.
I know you should use Poiseuille's Law, but what do you do about the pressures?

2. Oct 29, 2014

### Staff: Mentor

Do you know how to determine the pressure difference between the two locations in the pipe? If so, what is it?

Chet

3. Oct 29, 2014

### rlc

No, but I know it is part of Poiseuille's Law.

4. Oct 29, 2014

### Staff: Mentor

You don't need to use Poiseuille's law to find the pressure difference between the two locations in the pipe. You already have enough information to determine it. In those two vertical offshoots, is the fluid static or is it flowing?

Chet

5. Oct 29, 2014

### rlc

It would be static? Since it is open and the water wouldn't really go anywhere?

6. Oct 29, 2014

### rlc

Would the pressure difference just be H?

7. Oct 29, 2014

### Staff: Mentor

H is what we would call the difference in static pressure head. Do you remember the equation for static pressure as a function of depth? (It involves density and g).

Chet

8. Oct 29, 2014

### rlc

roh*g*h

9. Oct 29, 2014

### Staff: Mentor

Yes. That's right. Then what is the pressure difference between the two locations in the pipe in Pa?

Chet

10. Oct 29, 2014

### rlc

I'm sorry, but I don't know

11. Oct 29, 2014

### rlc

Wait, would it be density times velocity squared?

12. Oct 29, 2014

### Staff: Mentor

ρ=1000 kg/m3 (for water)
g = 9.8 m/s2
Δh= H = 0.0458 m
ΔP=ρgΔh (in units of Pa = kg/ms^2)

What do you get for ΔP?

13. Oct 29, 2014

### rlc

(1000)(9.8)(0.0458)=448.84 Pa

14. Oct 29, 2014

### rlc

Ah! That worked! Thank you so much!

15. Oct 29, 2014

### Staff: Mentor

Right. That's the pressure difference between the two locations.

Now, can you write down the Poiseulle equation for the pressure difference between the two locations in terms of the volumetric flow rate, the viscosity, the distance L, and the tube diameter D?

Chet

16. Oct 29, 2014

### rlc

Q=[(pi)R^4(roh*g*H)]/8nL

0.0125=(pi*R^4*448.84)/(8*1.00E-3*0.738)

R^4=5.23377E-8
R=0.015125 m
R=1.51 cm (which LONCAPA says is the correct answer)

Thank you so much for responding to me!