What is the ratio of the ratio of the absolute pressure at point A compared to point B if the open container shown below is filled with water?

A. P_{b }= 2P_{a}

B. P_{b }= 3P_{a}

C. P_{b }= 4P_{a}

D. P_{b }= 5P_{a}

##### Click for Explanation

This question is asking you to determine the ratio of the absolute pressure of Point B to Point A. To answer this question, you must determine the absolute pressure at each point. The absolute pressure is equal to the atmospheric pressure plus the gauge pressure, as shown in the equation, P_{abs }= P_{atm }+ P_{gauge}.

The atmospheric pressure exerted on the surface of the fluid is equal to 101,000 N/m^{2} (1 atm). To calculate the gauge pressure at each point, you must apply the formula, P_{gauge} = ρgh, where P_{gauge }is the pressure due to the water column of height h, ρ is the density of the fluid, g is the gravitational acceleration constant, and h is the depth.

P_{abs (A) }= P_{atm }+ P_{gauge (A)}

P_{abs (A) }= (101,000 N/m^{2})+ ρ_{water}gh_{A}

P_{abs (A) }= (101,000 N/m^{2}) + (1000 kg/m^{3})(10 m/s^{2})(10 m)

P_{abs (A)} = 201,000 N/m^{2}

^{ }

P_{abs (B) }= P_{atm }+ P_{gauge (B)}

P_{abs (B) }= (101,000 N/m^{2})+ ρ_{water}gh_{B}

P_{abs (B) }= (101,000 N/m^{2}) + (1000 kg/m^{3})(10 m/s^{2})(30 m)

P_{abs (B)} = 401,000 N/m^{2}

^{ }

**Therefore, the P _{B }= 2P_{A }making answer choice A the correct answer.** Furthermore, an increase in depth of 10 m in water equals 1 atmosphere. Therefore, the total pressure at A is 2 atm while the total pressure at B is 4 atm.

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