# How to Solve Manometer Problems With Fluids

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Fluid statics is the most basic form of fluid analysis, and manometry is one method of static fluid analysis. A manometer is a device that measures static fluid pressure. The three primary variables in a manometry problem are pressure, density and height of the fluid in the tubes. You must know at least two of these to solve a manometry problem. You must also use a common reference point when measuring your heights or the solution will be incorrect.

### Things You'll Need

• Calculator
• Define the variable you are looking for. In most manometry problems, you will most likely be looking for pressure. Fluid density is usually a known quantity once you know what the fluid is, and fluid height is often measured directly from the manometer.

Example: Find the pressure in an oil tank on the closed side of a u-shaped manometer.

• List what you already know about the problem. For any manometry problem, the fundamental equation is:

p2 - p1 = (rho)g(z2 - z1)

p = pressure at point 1 and 2: unknowns
z = height at points 1 and 2: to be measured
rho = fluid density: 1.5 slugs/ft^3 for the oil; 10 slugs/ft^3 for the manometer fluid)
g = acceleration of gravity: 32.2 in English units

• Use the fundamental equation to develop a specific equation for one side your manometry problem. In this example, it is the oil side. Start by identifying a reference line for your measurements. In a simple u-shaped manometer problem, this will often be where one fluid meets the manometer fluid. This lets you set z1 = 0.

p2 - p1 = (rho) 32.2 z2

The pressure in the oil then becomes:

p(oil) - p(z1) = 1.5 32.2 z2

p(oil) = (1.5 32.2 z2) + p(z1)

• Use the fundamental equation to develop a specific equation for the other side your manometry problem. In this example, it is the open side. Since by definition the pressure at z1 on the oil side is the same as the pressure at z1 on the open side, where p(atm) is the atmospheric pressure, you can write p(z1) as:

p(z1) - p(atm) = 10 32.2 (z3 -z1)

When using a manometer, you can simplify the calculations by writing all pressure values as gage pressure. This lets you set p(atm) = 0. Since z1 is the base line you defined earlier, it is also zero. Now you can rewrite the oil equation as:

p(z1) = 10 32.2 z3

• Combine the equations for both sides of the manometer

p(oil) = (1.5 32.2 z2) + p(z1)
p(z1) = 10 32.2 z3

p(oil) = (1.5 32.2 z2) + (10 32.2 z3)

• Fill in any missing information in the equation and solve. For this example, you need to find the values for z2 (the fluid height on the oil side) and z3 (the fluid height on the open side). These values can be taken or measured directly from the manometer and are therefore usually given in the problem statement.

z2 = 2
z3 = 4

p(oil) = (1.5 32.2 2) + (10 32.2 4)
p(oil) = 1190 slugs/ft^2

## References

• "Fluid Mechanics"; Merle C. Potter and John F. Foss; 1982
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