Question

A Venturi flowmeter is used to measure the flow rate of water (see the figure below). The flowmeter is inserted in a water pipe that has a diameter of 2 cm. At the narrow section, the diameter of the pipe is 0.8 cm. The U-tube contains oil with density 0.85 g/cm3. If the difference in the oil level on the two sides of the flowmeter is 1.5 cm, what is the volume flow rate of water through the pipe? The density of water is 1.0 g/cm3 oil 1.5 cm water 2.0 cm 0.80 cm flow Q-Number cmA3/s

Answer 1

The continuity equation is, A_1v_1 = A_2v_2 (1) p_1 + 1/2 rho v^2_1 = p_2 + 1/2 rho v^2_2 (2) From equation (1) v_2 = (A_1/A_2) v_1 Using Bernoulli's equation p_1 + 1/2 rho v^2_1 = p_2 + 1/2 rho (A_1/A_2)^2 v^2_2 (3) The pressure difference is, delta p = p_1 - p_2 From equation (3) delta p = 1/2 rho (A_1/A_2)^2 v^2_1 - 1/2 rho v^2_1 = 1/2 rho v^2_1 ((A_1/A_2)^2 - 1) v_1 = squareroot 2(delta p)/rho((A_1/A_2)^2 - 1) The volume flow rate in the tube is, Q = v_1A_1 = A_1 (squareroot 2(delta p)/rho ((A_1/A_2)^2 - 1) (4) Using hydrostatic law delta p = rho_0 gh Q = A_1 (squareroot 2(rho_0 gh)/rho((A_1/A_2)^2 - 1) (5) The flow rate of the fluid is delta p = rho_0 gh Q = (pi/4 d^2_1) (squareroot 2 (rho_0 gh)/rho ((d^2_1/d^2_2)^2 - 1) (6) = pi/2 (2.0 times 10^-2)^2 (squareroot (2) (850) (9.8) (1.5 times 10^-2))