1. Apr 11, 2010

### mparsons06

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

Water flows through a fire hose of diameter 7.15 cm at a rate of 0.019 m3/s. The fire hose ends in a nozzle of inner diameter 2.17 cm. What is the speed with which the water exits the nozzle?

2. The attempt at a solution:

So, I tried using Principle of Continuity:

A1 * v1 = A2 * v2

A = pi * d^2 / 4

A1 = 0.00402 m
A2 = 0.00037 m

A1 * v1 = A2 * v2
(0.00402 m) * (0.019 m^3/s) = (0.00037 m) * v2
0.0000764 m^4/s = (0.00037 m) * v2
v2 = (0.0000764 m^4/s) / (0.00037 m)
v2 = 0.206 m^3/s

Last edited: Apr 12, 2010
2. Apr 11, 2010

### rock.freak667

Assuming you typed the question properly, then 0.019 m3/s i not the velocity of the water entering the nozzle.

3. Apr 11, 2010

### mparsons06

So are you saying 0.019 m3/s is not my v1, but my v2? I'm confused.

4. Apr 11, 2010

### AtticusFinch

Think about it. Are those the units you would expect a velocity term to have?

5. Apr 11, 2010

### mparsons06

It would be m/s correct? But are my numbers correct? Or are my formulas wrong?

6. Apr 11, 2010

### AtticusFinch

Your equations are correct. What does the principal of continuity state should be continuous?

7. Apr 11, 2010

### mparsons06

It states that pressure is constant. But I'm still confused?

8. Apr 12, 2010

### AtticusFinch

That's not what the principle states. What physical quantity does A*v describe? (Look at the units)

9. Apr 12, 2010

### mparsons06

A*v describes the volume rate of low (m^3/s)... Right?

10. Apr 12, 2010

### AtticusFinch

Exactly, so the principle states that the volume flow rate is constant at any point.

Use that fact to answer the question.

11. Apr 12, 2010

### mparsons06

So is v1 = v2 = 0.019 m^3/s?

12. Apr 12, 2010

### AtticusFinch

Nope. You just realized that A*v (not v) is 0.019 m^3/s. Since this quantity must be conserved how would you find v2?

13. Apr 12, 2010

### mparsons06

A*v = 0.019 m^3/s
v = (0.019 m^3/s) / A = (0.019 m^3/s) / (3.14*(0.0217m)^2) = 12.9 m/s

Is that correct?

14. Apr 12, 2010

### AtticusFinch

Yes.

15. Apr 12, 2010

### mparsons06

It is wrong. I have no idea why. Ughhhh.

16. Apr 12, 2010

### AtticusFinch

Hmm that's odd. Are you sure you wrote the problem down correctly? Also, though I'm not sure whether this matters, but I'm getting 12.8 m/s rather than 12.9.

17. Apr 12, 2010

### mparsons06

Yes, I wrote it down right. I will 12.8, but I'm not sure if it'll make a difference. But anyways, thank you for all of your help. =) I really appreciate it.

18. Apr 12, 2010

### AtticusFinch

Ah I see what is wrong. The question gives you diameter not radius. Divide by 2 before finding the area.

19. Apr 12, 2010

### mparsons06

But do you really need radius if A = pi * d2 / 4?

20. Apr 12, 2010

### AtticusFinch

Well no, but you didn't divide by 4 when you used the diameter.