Fluid Statics

Overview


Fluid statics involves a special class of problems in fluid mechanics, where the fluid is not flowing. When the velocity of the fluid is zero everywhere, Newton’s law of viscosity shows that there are no shear forces in the fluid, since zero velocities imply zero velocity gradients in all directions. Thus, the only forces, which play a role in fluid statics, are pressure forces.

Some of the most interesting problems in fluid statics include:

  1. The variation of air properties in our atmosphere (or any other atmosphere for that matter). This variation is important to know, for example, to determine the performance of airplanes at altitude.
  2. The measurement of pressure using manometers (manometry) and other devices.
  3. The calculation of hydrostatic forces in submerged surfaces. This application is of paramount importance to civil engineers, who often have to design huge dams to withhold billions of cubic meters of water.
  4. Buoyancy with its applications in naval architecture as well as in aviation (balloons). On a smaller scale, Archimedes’ principle (buoyancy) is used in the design of hydrometers, which measure the specific weight of fluids. A hydrometer is used, for example, to tell whether there is enough antifreeze in the radiator of your car, to be able to withstand subfreezing temperatures.

 

Learning Objectives

By the end of this unit, you should be able to:
1 Define and distinguish between absolute pressure, gage pressure, and vacuum.

2 Explain Blaise Pascal's law of pressure transmission.
3 Derive the basic differential equation of hydrostatics starting with the equilibrium of a fluid element.
4 Derive the equation for the pressure variation of a uniform-density fluid.
5 Identify, formulate and solve problems involving manometers.

Discussion Questions

1 What is (fluid) pressure and where does it come from?
2 Define the following:

    a. absolute zero pressure:

    b. absolute pressure:

    c. gage pressure:
3 State Blaise Pascal’s law.  Think of and discuss at least 2 engineering applications of this law, from things you have seen or experienced.
4 SCUBA anyone? At what rate does the pressure increase as you go down in ocean water?  What happens to your lungs as you go down in the water (free dive)?  How does SCUBA work?
5 How do hydraulic lift devices (like the ones used at gas stations to raise cars) work? 
6 How does the pressure of a liquid vary with its depth (i.e., in what fashion)?
7 State Archimedes’ principle.  Think of and discuss at least 2 engineering applications of this law, from things you have seen or experienced.
8 What do we mean by "center of pressure" of a submerged surface?  Why do we care to know?
9 Why dams are built thicker at the bottom?

Applications

1 Absolute pressure and gage pressure.
2 Hydrostatic equation; Manometry / Pascal's Law.
3 Hydrostatic Forces on Submerged Surfaces.
4 Archimedes' Principle (Buoyancy); Hydrometry.

Links

This link contains air properties in a standard atmosphere.
1. Standard Atmosphere Calculator