Question

(a) Calculate the absolute pressure at the bottom of a fresh-water lake at a depth of 22.8 m. Assume the density of the water is 1.00 ✕ 10³ kg/m³ and the air above is at a pressure of 101.3 kPa.
Pa

(b) What force is exerted by the water on the window of an underwater vehicle at this depth if the window is circular and has a diameter of 34.0 cm?

Answer 1

a) The Pressure inside a liquid is given by the following formulae :

where,

• P is the pressure due to liquid.
• is the density of the liquid
• g is the acceleration due to gravity
• and h is the depth inside the liquid.

# Now in the given question we have;

• Depth inside the liquid, h = 22.8 m
• The Density of the water, = 1.00*10³ Kg/m³

so, the pressure due to the water at 22.8 m would be

the value of acceleration due to gravity 'g', we are taking here is 9.8 m/s²

since Pascal (Pa) in simpler units is Kg/m.s²

^therefore,

Now, this pressure is the pressure exerted by the water. But the total pressure inside the water would be the sum of pressure of the water (which we have calculated above) and the air pressure above the water.

so,

since 1 kPa = 1000 Pa

so, 101.3 kPa = 101300 Pa

Therefore, the absolute pressure at the bottom of a fresh-water lake at a depth of 22.8 m is 324740 Pa or 324.74 kPa.

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(b)

since the pressure exerted by any substance is given by

therefore,

Now, we have already calculated the Pressure in part (a). Also, we have given the diameter of the circular window from which we can calculate the area.

where d is the diameter of the circular window.

we have given,

• the diameter of circular window = 34.0 cm = 0.34 m

so,

Now, we have both, the area and the pressure. therefore we can calculate the force as follows:

Therefore, the force exerted by the water on the window of an underwater vehicle is 29483.794 N.

Thank You.