# Fluid Mechanics 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 + rho*gh

P1 = Patm + rho1*gh1 + rho2*gh2 + rho3*gh3

Patm = rho*gh (Atmospheric pressure is measured by a device called a barometer; thus, the atmospheric pressure is often referred to as the barometric pressure. [Remember that the atmospheric pressure at a location is simply the weight of the air above that location per unit surface area. Therefore, it changes not only with elevation but also with weather conditions]) INTRODUCTION TO FLUID STATICS: Fluid statics deals with problems associated with fluids at rest. The fluid can be either gaseous or liquid. Fluid statics is generally referred to as hydrostatics when the fluid is a liquid and as aerostatics when the fluid is a gas. In fluid statics, there is no relative motion between adjacent fluid lay- ers, and thus there are no shear (tangential) stresses in the fluid trying to deform it. The only stress we deal with in fluid statics is the normal stress, which is the pressure, and the variation of pressure is due only to the weight of the fluid. HYDROSTATIC FORCES ON SUBMERGED PLANE SURFACES: A plate exposed to a liquid, such as a gate valve in a dam, the wall of a liquid storage tank, or the hull of a ship at rest, is subjected to fluid pressure distributed over its surface (Fig. 3–23). On a plane surface, the hydrostatic forces form a system of parallel forces, and we often need to determine the magnitude of the force and its point of application, which is called the center of pressure. In most cases, the other side of the plate is open to the atmosphere (such as the dry side of a gate), and thus atmospheric pressure acts on both sides of the plate, yielding a zero resultant. In such cases, it is convenient to subtract atmospheric pressure and work with the gage pressure only (Fig. 3–24). For example, Pgage = rho*gh at the bottom of the lake.

Then the absolute pressure at any point on the plate is P = P0 + rho*gh = P0 + rho*gy sin \theta

The point of intersection of the line of action of the resultant...

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