Calculate Height of Manometer with 70KN/m^2 Diff Pressure

In summary, using the formula for a well type manometer, the height of the measuring column can be calculated by setting the applied differential pressure to be equal to the product of the weight density, acceleration of gravity, height, and the ratio of the tube and well areas plus 1. In this conversation, the height of the measuring column is found to be 52.39573354mm when the applied differential pressure is 70KN/m^2 and the sealing liquid is mercury with a weight density of 132.5 KN/m^3. However, it should be noted that the correct answer is 527mm and the error in the calculation was due to including the acceleration of gravity twice.
  • #1
Mongster
20
7
In a reservoir of a well type manometer, the sealing liquid is mercury having a weight density of 132.5 KN/m^3. If the area of the well is 0.02m^2 and that of the tube is 40mm^2. Calculate the height of the measuring column if the applied differential pressure is 70KN/m^2.

Relevant formulae: P1-P2
=ρ.m(g)(h)(a2/a1 + 1)

Attempt at question.

70=132.5(9.81)(h)(0.00004/0.02 + 1)
70=1335.98664(h)
h=0.05239573354m
=52.39573354mm

Set up is similar as shown below

The answer provided is 527mm. I can't spot any mistakes in my calculations too.
Well-Type-Manometer.jpg
 
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  • #2
Well, for one thing, you don't need the factor of 9.81 since that is already included in the "weight density" 132.5kN/m^3.

Chet
 
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Likes Mongster
  • #3
Hey thanks a lot for pointing that out! Didn't realize I've made such a silly error. :D
 

FAQ: Calculate Height of Manometer with 70KN/m^2 Diff Pressure

How do you calculate the height of a manometer?

To calculate the height of a manometer, you need to use the equation: height = pressure/density x gravity. In this case, the pressure is given as 70KN/m^2 and the density is the density of the fluid used in the manometer. Gravity is typically 9.8 m/s^2 for Earth. Plug in these values to solve for the height.

What is the purpose of calculating the height of a manometer?

The height of a manometer is used to measure the pressure difference between two points in a fluid system. This can be helpful in determining flow rates or detecting any leaks or blockages in the system.

What units should be used for the pressure and height in the calculation?

The units used for pressure and height in the calculation should be consistent. In this case, the pressure is given in kilonewtons per square meter (KN/m^2) and the resulting height will be in meters (m).

How does the height of the manometer change with different pressure values?

The height of the manometer is directly proportional to the pressure difference. This means that as the pressure increases, the height of the manometer will also increase. Similarly, if the pressure decreases, the height will decrease as well.

What other factors can affect the height of a manometer?

Aside from pressure and density, the height of a manometer can also be affected by the type of fluid and the shape and size of the manometer. These factors can impact the accuracy of the measurement and should be taken into consideration when using a manometer to calculate pressure difference.

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