Question

A liquid is poured into a U-tube as shown in the figure below. The left arm of the tube has cross sectional area A1 of 20.0 cm2, and the right arm has a cross-sectional area A2 of 10.0 cm2. 0.200 kg of water is then poured into the right arm as shown. The liquid rises in the left arm by a distance h = 2.15 cm. The density of water is 1.00 × 103 kg/m3. (a) Determine the length of the water column in the right arm of the U-tube. (b) Determine the density of the liquid.

Watcr 9 사 - Liquid

Answer 1

Given implies A_1 = 20 cm^2, A_2 = 10 cm^2, m_w = 0.2 kg h = 2.15 cm, rho_w = 10^3 kg/m^2, g = 9.81 m/s^2 (a) length of water column implies m_w = rho_w A_2 L_w implies 0.2 = 10^3 times 10 times 10^-4 L_w L_w = 0.2 m \r\n balancing pressure at horizontal line meeting water and liquid rho_w g L = rho g (h + x) {where, A_2 x = A_1 h} rho_w g L = rho g [h + A_1 h/A_2] 10^3 times 0.2 = rho [0.0215 + 20/10 times 0.0215] rho = 3100.78 kg/m^3