# PSV: Calculate pressures using a manometer

### Pressure

Pressure and temperature are two of the most important of chemical engineering process variables.

In addition to reminding you a bit about them, it is importnat to discus how one might find out what they are in a given process!

DEFINITION:

Pressure is the ratio of force to the area over which that force acts (or the area over which that force is transmitted).

What ar the units of pressure then?

Pressure on a solid surface is easy to follow.

The pressure in a fluid is tougher. One way to think of it:

DEFINITION:

Hydrostatic Pressure is the pressure in a fluid due solely to the fluid's weight. [$\rho g h$].

EXERCISE:

Check the dimensions on $\rho g h$.

NOTE:

For this reason, pressure is sometimes given in terms of fluid height instead of regular pressure units. (e.g., "mmHg" or "ft of water")

Pressure measurements:

Manometers

OUTCOME:

Calculate pressures using a manometer (and explain the concept of gauge pressure)

TEST YOURSELF!

If we know P2 and the difference in fluid heights, how do we calculate P1?

Hydrostatic Pressure

Consider a cylindrical tank filler with water:

We want to measure the hydrostatic pressure on the bottom of the tank.

Volume of cylinder (fluid): $\pi r^2h$
Weight of fluid: $\rho g V$
Area of base: $\pi r^2$

Pressure on Base: F/A -> $\frac{\rho g(\pi r^2h)}{\pir^2}$ -> $\rho g h$

So, hydrostatic pressure is independent of radius of cylinder!