Venturi Meter with Bernoulli's

[Gorz]

Homework Statement

Water flows through a venturi meter, with an inlet diameter of 25cm and a throat diameter of 15cm. The pressure difference is measured using a manometer, which displaces the mercury by 12mm on the throat side.

Homework Equations

Bernoulli's
Mass continuity
P=rho.g.h

The Attempt at a Solution

Is this correct? I have no answers available as its from a past paper. My exam is tommorow and I would just like to clarify that the method I have used to find the pressure difference is correct.

Thanks.

 

[Gorz]

No one able to help with this?

My exam is tommorow morning and I wouldn't mind some closure on my quiery.

 

[nlightner]

I would first like to commend you for seeking clarification on your solution before your exam. It shows a strong understanding of the importance of accuracy and precision in scientific work.

To answer your question, your approach seems to be correct. You have used Bernoulli's equation, which states that the total energy of a fluid remains constant throughout its flow, as long as there is no energy added or removed from the system. In this case, the fluid is water and the energy is in the form of pressure.

To find the pressure difference, you have correctly used the equation P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the fluid column in the manometer. This equation is derived from the hydrostatic equation, which states that the pressure at any point in a fluid is equal to the weight of the fluid column above it.

In your case, you have correctly identified that the pressure difference between the inlet and throat of the venturi meter can be found by measuring the height of the fluid column displaced by the manometer. This height is directly proportional to the pressure difference, and by using the given values for the inlet and throat diameters, you can calculate the pressure difference using the equation P = ρgh.

In conclusion, your method for finding the pressure difference using Bernoulli's equation and the hydrostatic equation is correct. I wish you the best of luck on your exam tomorrow!