# Homework Help: Venturi / Flow Rate

1. Apr 10, 2007

### LikwidN2

1. The problem statement, all variables and given/known data
• Known/Given
• Water flows through a Venturi meter (mercury [density=13.6E3 kg/m^3] in the manometer).
• Pipe size: 10.0cm diameter
• Constriction size: 5.6cm diameter
• Height difference of mercury: 2.3cm
• Unknown - Flow Rate (L/s)

2. Relevant equations
• Bernoulli's - P1 + (1/2)*d*V1^2 = P2 + (1/2)*d*(V2)^2
• Flow Rate - I = A1*V1 = A2 * V2
• Pressure drop - the book has this exact example, and says that P1 - P2 = (D_fluid [water] - D_liquid [mercury])*g*H
However, I don't understand why the pressure drop isn't just:
D_mercury*g*H

3. The attempt at a solution
Using the book's guided steps:
• V2 = (A1/A2)*V1
• P1 - P2 = (1/2)*D_water*((A1/A2)^2-1)*V1^2
• (1/2)*D_water*((A1/A2)^2-1)*V1^2 = (D_water - D_mercury)*g*H
• v1 = 0.7875m/s
• v1 = 78.75cm/s
• Flow = 78.75 * pi * (10cm/2)^2 = 6185 cm^3/s
• 6185 cm^3/s * ([1 L/s] / [1000^3 cm^3/s]) = .03825 L/s

This is off everyone's favorite online homework system, WebAssign, and I have used 5/6 submissions I'm terribly sorry for the awful formatting, but I don't have access to a good typesetting program as of yet (downloading TeX as we speak [well... as I type]).

Last edited: Apr 10, 2007
2. Apr 10, 2007

### denverdoc

I agree that you should just use the delta P given in 23mm Hg. See what answer you come up with and we can look that over before No 6 submission.

3. Apr 11, 2007

### LikwidN2

After confirming with a friend, I realized that I just had the conversion factor wrong. Their method worked, and apparently m^3/s * 1000 = L/s. Unfortunately, this leaves me no closer to understand why they used the two densities and not just the mercury density. With a lot of luck I might be able to extract a coherent [say: in English] answer from my TA, but probably not.

4. Apr 11, 2007

### denverdoc

anychance you can post a picture if given? I get 6.42L/s using just 23mmHg for delta P

5. Apr 11, 2007

### LikwidN2

Picture

The correct answer turned out to be 12.7 L/s. I get everything except for the use of the change in densities.

Thanks for all your help, by the way, I appreciate it! To think of my 40k / year tuition and I need to find help online from a helpful stranger.

6. Apr 11, 2007

### denverdoc

Thats too funny and sad at the same time. I went to school when many of the TA's still spoke english.

anyhow, all i know is that the delta p and rho need to be in the same units as you cant mix and match say mm Hg with density of water in g/ml etc. Let me know if you get a good explanation.