Chapter 15, Problem 52PQ

Figure P15.52 shows a Venturi meter, which may be used to measure the speed of a fluid. It consists of a Venturi tube through which the fluid moves and a manometer used to measure the pressure difference between regions 1 and 2. The fluid of density ${\rho }_{\text{tube}}$ moves from left to right in the Venturi tube. Its speed in region 1 is v₁, and its speed in region 2 is v₂. The neck’s cross-sectional area is A₂, and the cross-sectional area of the rest of the tube is A₁. The manometer contains a fluid of density ${\rho }_{\text{mano}}$.

a. Do you expect the fluid to be higher on the left side or the right side of the manometer?

b. The speed v₂ of the fluid in the neck comes from measuring the difference between the heights (y_R − y_L) of the fluid on the two sides of manometer. Derive an expression for v₂ in terms of (y_R − y_L), A₁, A₂, ${\rho }_{\text{tube}}$, and ${\rho }_{\text{mano}}$.

FIGURE P15.52