The Basic Manometer

Ch 1, Lesson E, Page 5 - The Basic Manometer

• The U-shaped tube attached to the tank in this diagram is called a manometer.
• In this case, the tank contains gas and we would like to determine the pressure in the tank based on the manometer reading, h.
• If the tank contains a gas and the manometer and the tank are not extremely tall, then the pressure in the tank and the pressure at point 1 are approximately equal.
• How does that help us ?
• Well, let’s consider the relationship between the pressure at point 1 and the pressure at point 3.
• We can use the barometer equation to relate P2 to P1 and again to relate P2 to P3.
• When we do, we discover that P1 = P3.
• Is this always true when two points are at the same elevation ?  Not quite.
• The two points must be at the same elevation.  They must be connected by a STAGNANT fluid and all of the fluid in the path that connects the two points must have the same density.
• In this case, we meet all of these criteria, so P3 does indeed equal P1 which equals Ptank.
• So, now all we need to do is use the barometer equation to relate P3 to P4 and we have our answer, which is known as the manometer equation.
• If P4 is atmospheric pressure because the right leg of the manometer is open , then Ptank exceeds atmospheric pressure by
  ρm g/gc h.
• In other words, rm g/gc h is the gage pressure of the tank !
• Cool, now let’s take a look at another type of manometer.