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 2.00 m/s. 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

Using Bernoulli's equation, we have:

P_A + (1/2)*rho*v_A^2 + rho*g*h = P_B + (1/2)*rho*v_B^2

Solving for h, we get:

h = (P_A - P_B)/(rho*g) - (1/2)*[(v_B/v_A)^2 - 1]

We can assume that the pressure at A and B are the same (since they are at the same height). Thus:

h = (rho*g/2)*[(A_B/A_A)^2 - 1]

Substituting the given values, we get:

h = (1000 kg/m^3)*(9.81 m/s^2)/2)*[(16 cm^2/25 cm^2)^2 - 1]

h = 0.0216 m = 2.16 cm

Therefore, the answer is D) 2.16 cm.

Water Flows in the Horizontal Pipe Shown in the Figure