At what depth in sea water is the gauge pressure equal to 1 atm? The density of sea water is 1.03 $\times$ 10³ kg/m³. A)5 m B)7.5 m C)10 m D)15 m E)20 m

Question

Quizplus · Accepted Answer

The gauge pressure at any depth h in a fluid with density ρ is given by:

P_gauge = ρ*g*h

where g is the acceleration due to gravity, and h is the depth measured from the surface of the fluid.

At the depth where the gauge pressure is equal to 1 atm (which is approximately equal to the atmospheric pressure at the surface), we have:

P_gauge = 1 atm = 1.01325*10^5 Pa

ρ = 1.03*10^3 kg/m^3 (density of sea water)

g = 9.81 m/s^2 (acceleration due to gravity)

Therefore, we can solve for the depth h:

1 atm = ρ*g*h

h = 1 atm / (ρ*g)

h = 1.01325*10^5 Pa / (1.03*10^3 kg/m^3 * 9.81 m/s^2) ≈ 10 m

So, the best choice is C) 10 m, as this is the depth at which the gauge pressure in sea water is equal to 1 atm.

At What Depth in Sea Water Is the Gauge Pressure ×\times×

At What Depth in Sea Water Is the Gauge Pressure $\times$