(a) Using Bernoulli's equation, show that the measured fluid speed v for a pitot tube, like the one in Figure 12.7 (b), is given by where h is the height of the manometer fluid, is the density of the manometer fluid, is the density of the moving fluid, and g is the acceleration due to gravity. (Note that v is indeed proportional to the square root of h, as stated in the text. (b) Calculate v for moving air if a mercury manometer's h is 0.200m.
Figure 12.7 Measurement of fluid speed based on Bernoulli's principle. (a) A manometer is connected to two that are close togeter and small enough not to disturb the flow. Tube 1 is open at the end facing the flow. A dead spot having zero speed is created there. Tube 2 has an opening on the side, and so the fluid has a speed V across the opening; thus, pressure there drops. The difference in pressure at the manometer is , and so h is proportional to .
(b) This type of velocity measuring device is a Prandtl tube, alos known as a pitot tube.
