Chapter 13, Problem 69GP

Venturi meter. The Venturi meter is a device used to measure the speed of a fluid traveling through a pipe. Two cylinders are inserted in small holes in the pipes, as shown in Figure 13.46. Since the cross-sectional area is different at the two places, the speed and pressure will be different there also. The difference (h) in the heights of the two columns can easily be measured, as can the cross-sectional areas A₁ and A₂. Notice that points 1 and 2 in the figure are both at the same vertical height, (a) Show that Δp = ρgh, where ρ is the density of the fluid and Δp is the pressure difference between points 1 and 2. (b) Apply Bernoulli’s equation and the continuity condition to show that the speed at point 1 is given by the equation

Figure 13.46

Problem 69

$v_1=\sqrt{\frac{2gh}{{(A_1/A_2)}^2-1}}.$

(c) How would you find the speed at point 2?