Bernoulli's principle: 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

Applying Bernoulli's principle between points A and B, we have:

P + 1/2ρv² + ρgh = constant

Since the pipe is horizontal, we can neglect the term involving the height difference (h) between A and B. Also, we will assume that the pressure at A and B is atmospheric pressure (since the problem does not provide any other information). Thus, we have:

1/2ρAvA² = 1/2ρBvB²

Solving for vB, we get:

vB = √(AvA²/B)

Substituting the given values, we get:

vB = 2.50 m/s

Now, we can apply Bernoulli's principle again between points B and C (the top of the mercury column in the right arm of the manometer).

P + 1/2ρv² + ρgh = constant

Since the fluid in the manometer is mercury, we need to use its density to calculate the pressure difference between points B and C. Thus, we have:

P + 1/2ρBvB² = P + ρHggh

Solving for h, we get:

h = vB²/(2gρHg)

Substituting the given values, we get:

h = 0.0216 m = 2.16 cm

Therefore, the answer is D.

Bernoulli's Principle: Water Flows in the Horizontal Pipe Shown in the Figure