At a depth of 5 meters, the pressure in a tank of water is equal to 1.5 atm. What is the pressure at a depth of 20 meters?
A) 3 atm
B) 4 atm
C) 5 atm
D) 6 atm
This question is testing your understanding of the relationship between total pressure, atmospheric pressure, and gauge pressure: Ptotal = Patm + Pgauge. To begin, you must know that Patm results from the pressure of the atmosphere and Pgauge results from the pressure due to the fluid. To calculate the gauge pressure, you can use the equation Pgauge = rgd, where r is the density of the fluid, g is gravity, and d is the depth below the surface of the fluid.
At a depth of 5 meters, Pgauge = rgd = (1000 kg/m3)(10 m/s2)(5 m) = 50,000 N/m2 or ~0.5 atm. Therefore, the Patm is equal to 1 atm. Thus, at a depth of 20 m, Ptotal = Patm + Pgauge = 1 atm+ (1000 kg/m3)(10 m/s2)(20 m) = 3 atm, making A the correct answer.