Fluid Mechanics by Martin Widden (auth.)

By Martin Widden (auth.)

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This demonstrates the truth of Archimedes' Principle. Here is a straightforward example for you to try: the volume of a small submarine is 30 m". When it is completely submerged in sea-water of density 1025 kg/m", what is the magnitude of the upthrust experienced by the submarine? The upthrust is equal to the weight of fluid displaced, remember. 81 x 30 = Pwater = 302 X 103 N X = 302 kN Archimedes' Principle applies just as well for bodies immersed in a gas. Here is an example. A balloon filled with helium is to be used to lift a weather sensor/transmitter to the upper atmosphere.

When the liquid in the U-tube has settled to its position and is at rest, the pressure at any two points at the same level within the liquid will be the same. 35 Liquid of density p A U-tube manometer is shown connected to a pipe. The liquid, of density p, fills both the pipe and the lower part of the U-tube. One leg of the U-tube is open to the atmosphere, so the pressure at the surface of the liquid (point A) is atmospheric; if measured as a gauge pressure, its value is zero . At point C, which is a distance h lower than A, the gauge pressure is Pc, which is equal to .

31 FLUID MECHANICS 52 I (PI - pz) = (p - Pm)gh I Working: the pressures at C and D are Pc = PA + pgh and PD = PB + Pmgh. Because A and B are at the same level in the same body of liquid we know that PA = PB. Therefore (Pc - PD) = (p - Pm)gh. Below the level of C and D both limbs are full of the same fluid (water) and so the pressure difference remains the same at any level. Thus (PI - pz) = (Pc - PD) = (p - Pm)gh 53 Sometimes the fluid whose pressure we wish to measure is a gas. The density P of a gas is so much smaller than the density of the liquid in the manometer tube that it is often reasonable to ignore it.

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