Fluid Mechanics Notes
EXAM 1 NOTES
The actual pressure at a given position is called the absolute pressure, and it is measured relative to absolute vacuum (i.e., absolute zero pressure). Most pressure-measuring devices, however, are calibrated to read zero in the atmosphere (Fig. 3–2), and so they indicate the difference between the absolute pressure and the local atmospheric pressure. This difference is called the gage pressure. Pgage = Pabs - Patm
The pressure at a point in a fluid has the same magnitude in all directions. (Pressure is a scalar)
Variation of Pressure with Depth
It will come as no surprise to you that pressure in a fluid at rest does not change in the horizontal direction. This can be shown easily by considering a thin horizontal layer of fluid and doing a force balance in any horizontal direction. However, this is not the case in the vertical direction in a gravity field. Pressure in a fluid increases with depth because more fluid rests on deeper layers, and the effect of this “extra weight” on a deeper layer is balanced by an increase in pressure For a given fluid, the vertical distance \Delta z is sometimes used as a measure of pressure, and it is called the pressure head.
If we take the top of a fluid to be at the free surface of a liquid open to the atmosphere, where the pressure is the atmospheric pressure Patm, then the pressure at a depth h from the free surface is: P = Patm + \rho *gh or Pgage = \rho *gh
Liquids are essentially incompressible substances, and thus the variation of density with depth is negligible. This is also the case for gases when the elevation change is not very large. at great depths such as those encountered in oceans, the change in the density of a liquid can be significant because of the compression by the tremendous amount of liquid weight above.
For fluids whose density changes significantly with elevation, a relation for the variation of pressure with elevation can be obtained: dP/dz = rho*g
P2 = Patm +
The actual pressure at a given position is called the absolute pressure, and it is measured relative to absolute vacuum (i.e., absolute zero pressure). Most pressure-measuring devices, however, are calibrated to read zero in the atmosphere (Fig. 3–2), and so they indicate the difference between the absolute pressure and the local atmospheric pressure. This difference is called the gage pressure. Pgage = Pabs - Patm
The pressure at a point in a fluid has the same magnitude in all directions. (Pressure is a scalar)
Variation of Pressure with Depth
It will come as no surprise to you that pressure in a fluid at rest does not change in the horizontal direction. This can be shown easily by considering a thin horizontal layer of fluid and doing a force balance in any horizontal direction. However, this is not the case in the vertical direction in a gravity field. Pressure in a fluid increases with depth because more fluid rests on deeper layers, and the effect of this “extra weight” on a deeper layer is balanced by an increase in pressure For a given fluid, the vertical distance \Delta z is sometimes used as a measure of pressure, and it is called the pressure head.
If we take the top of a fluid to be at the free surface of a liquid open to the atmosphere, where the pressure is the atmospheric pressure Patm, then the pressure at a depth h from the free surface is: P = Patm + \rho *gh or Pgage = \rho *gh
Liquids are essentially incompressible substances, and thus the variation of density with depth is negligible. This is also the case for gases when the elevation change is not very large. at great depths such as those encountered in oceans, the change in the density of a liquid can be significant because of the compression by the tremendous amount of liquid weight above.
For fluids whose density changes significantly with elevation, a relation for the variation of pressure with elevation can be obtained: dP/dz = rho*g
P2 = Patm +