Understanding the Conversion Formula for Venturimeter Readings

[ujjwal kapil]

Hi all

I was trying to solve some numerical problems on venturimeter. I got stuck due to a formula, that I was not able to make sense of. It is a conversion of reading of differential manometer in mercury to corresponding reading in water. I've attached the question, please help me understand it.

 

[NascentOxygen]

Hi ujjwal kapil. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

Draw a U-tube manometer showing a difference in mercury levels. Now, add water above both surfaces of mercury, and show pressures of P1 and P2 acting on that water.

Apply your ρgh formula, etc., and derive the pressure differential P2 - P1 in terms of the other quantities present. Write your working here.

 

[ujjwal kapil]

I have found an answer, but not in accordance with the solution.
20cm of Hg= 272cm of H2O, but it is given as 252 in the solution.

 

[NascentOxygen]

Keep it simple, draw a symmetrical U-tube.

You overlooked the water! On one side you have P1 and a column of h metres of H₂O balanced on the other side by P2 and a column of h metres of Hg.

So try this again. Keep it as algebra, don't substitute numbers. We're aiming towards that expression you circled, remember?

 

[rezeew]

Hello,

Thank you for reaching out with your question about venturimeter calculations. I understand that you are having trouble understanding a formula related to converting readings from a differential manometer in mercury to water.

First, it is important to understand the purpose of a venturimeter. It is a device used to measure the flow rate of a fluid, typically in a pipe or a channel. The differential manometer is used to measure the pressure difference between two points in the venturimeter, which is then used to calculate the flow rate.

Now, to address your question about the conversion of readings from mercury to water. This is necessary because the density of mercury and water are different, therefore the pressure readings will also be different. The formula for converting the readings is based on the principle of hydrostatics, which states that the pressure at a certain depth in a fluid is directly proportional to the density of the fluid.

I would recommend reviewing the principles of hydrostatics and practicing some sample problems to better understand the conversion formula. You can also consult your textbook or reach out to your instructor for further clarification.

I hope this helps to clear up your doubts. Keep practicing and asking questions, and you will soon master the calculations for venturimeter. Best of luck!