Water flows in the horizontal pipe shown in the figure.At point A the area is 25.0 cm² and the speed of the water is At B the area is 16.0 cm².The fluid in the manometer is mercury,which has a density of 13,600 kg/m³.We can treat water as an ideal fluid having a density of 1000 kg/m³.What is the manometer reading h? A) 0.546 cm B) 1.31 cm C) 2.81 cm D) 2.16 cm E) 3.36 cm

Question

Quizplus · Accepted Answer

To solve the problem, we can use the Bernoulli's equation, which relates the pressure, height, and speed of a fluid at two different points along a stream line. 
At point A, we have:

P_A + 1/2 ρv_A^2 + ρgh_A = P_0 + ρgh_m

where P_A is the pressure at point A, v_A is the velocity at point A, h_A is the height of point A from a reference level, P_0 is the atmospheric pressure, ρ is the density of water, and h_m is the height of the mercury column in the manometer.

Similarly, at point B, we have:

P_B + 1/2 ρv_B^2 + ρgh_B = P_0 + ρgh_m

where P_B is the pressure at point B, v_B is the velocity at point B, and h_B is the height of point B from the same reference level as h_A.

Since the pipe is horizontal, we have h_A = h_B and we can subtract the two equations to eliminate the atmospheric pressure and the heights:

1/2 ρv_A^2 - 1/2 ρv_B^2 = (ρ - 13.6×10^3 kg/m^3)gh

where h is the height difference between the water level in the pipe and the mercury column in the manometer.

Solving for h, we get:

h = (v_A^2 - v_B^2)/(2g(ρ - 13.6×10^3 kg/m^3)) 
= (0.11^2 - 0.16^2)/(2×9.8×(1000 - 13600) kg/m^3) 
≈ 0.0216 m ≈ 2.16 cm

Therefore, the answer is (D).

Water Flows in the Horizontal Pipe Shown in the Figure