A water line enters a house 2.0 m below ground. A smaller diameter pipe carries water to a faucet 5.0 m above ground, on the second floor. Water flows at 2.0 m/s in the main line and at 7.0 m/s on the second floor. Take the density of water to be 1.0 x10³ kg/m³. The diffenernce in pressure in the main line is 2.0 x 10⁵ Pa, then the pressure on the second floor is: A) 7.5 x 10⁴ Pa with the main line at the higher pressure B) 2.65 x10⁴ Pa with the main line at the higher pressure C) 7.5 x 10⁴ Pa with the main line at the lower pressure D) 2.65 x 10⁴ Pa with the main line at the lower pressure E) 9.4 x 10⁴ Pa with the main line at the higher pressure

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Quizplus · Accepted Answer

The pressure difference is due to the difference in height between the two points. The pressure is higher at the lower point because there is more water above it pushing down. The difference in pressure is given by:$$P = \rho g h$$where:* P is the pressure difference (Pa)* ρ is the density of water (kg/m^3)* g is the acceleration due to gravity (m/s^2)* h is the height difference (m)In this case, the height difference is 5.0 m - 2.0 m = 3.0 m. The pressure difference is:$$P = (1.0 x 10^3 kg/m^3)(9.8 m/s^2)(3.0 m) = 2.94 x 10^4 Pa$$The pressure on the second floor is therefore:$$P_2 = P_1 + P = 2.0 x 10^5 Pa + 2.94 x 10^4 Pa = 2.29 x 10^5 Pa$$The pressure on the main line is therefore:$$P_1 = P_2 - P = 2.29 x 10^5 Pa - 2.94 x 10^4 Pa = 2.0 x 10^5 Pa$$Therefore, the pressure on the second floor is 7.5 x 10^4 Pa with the main line at the higher pressure.

A Water Line Enters a House 2