Question

A U-tube open at both ends is partially filled with water (see figure) (Pair 1.29 kg/m ) Oil having density 725 kg/m2 is then poured into the right arm and forms a column L = 5.58 cm high. Shield Po Water Oil a) Determine the difference h in heights of the two liquid surfaces. Number Units b)The right arm is then shielded from any air motion while air is blown across the top of the left arm until the surface of the two liquids are at the same height. Determine the speed of the air being blown across the left arm. (Pair 1.29 kg/m2 ) Number Units

Answer 1

rho_air = 1.29 kg/m^3 density of oil rho_oil = 725 kg/m^3 L = 5.58 cm density of water = 1000 kg/m^3 a) pressure at level AA' is equal in both column. P_A = P_0 + rho_w g (L - h) P_B = P_0 + rho_oil g L P_A = P_B P_0 + rho_w g (L - h) = P_0 + rho_oil g L rho_w g L - rho_w g h = rho_oil g L rho_w g L = rho_w g L - rho_oil g L h = (rho_w - rho_oil) L/rho_w h = (1000 - 725)/1000 times 5.58 h = 1.395 cm b) pressure difference of height h is compensated by pressure due to flow of air so 1/2 rho_air V^2 = rho_w g h v^2 = 2 rho_w g h/rho_air \r\n V = squareroot 2 rho_w g h/rho_air = squareroot 2 times 1000 times 10 times 1.395/1.29 V = 147.06 m/s c) cross sectional Area at A = 28.5 cm^2 Speed of water at A =