By Martin Widden (auth.)
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Extra resources for Fluid Mechanics
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. L Returning to the equation we derived in Frames 40 and 41, the gauge pressure P in the pipe is given by P = Pmgh l - pghz = g(Pmhl - phz) The density of liquids used in manometers ranges from around 800 kg/m!
To the height h. 35 FLUID MECHANICS 60 Finally in this section, we must mention the mercury barometer, which is often used to measure atmospheric pressure in the laboratory. The simplest form is just a glass tube closed at one end , filled with mercury and inverted so that its open end is below the surface of a bath of mercury. B I :. h 1 A The pressure at the surface of the mercury in the open bath is atmospheric, so the pressure is also atmospheric at point A, at the same level in the same continuous, stationary body of mercury.
Suppose a clean glass tube of 1 mm bore is dipped into a beaker of water. The temperature is 20 "C, and so the surface tension of water is 74 x 10- 3 N/m. If the angle of contact is 0 = 15°, how far up the tube does the water rise? 029 m This phenomenon, whereby liquid can rise quite substantial distances up a narrowbored tube, can cause significant errors when using such tubes to measure pressures etc. This is one reason why tubes as narrow as 1 mm bore are only rarely used, but even with the more common sizes of 6 mm diameter upwards the error can be as much as 5 mm, which is still serious.
Fluid Mechanics by Martin Widden (auth.)