Problem: A person is diving in a lake in the depth of h = 9.5 m. The density of the water is ρ = 1.0×103 kg/m3. The pressure of the atmosphere is P0 = 1.0×105 Pa. The surface area of the top of the person’s head is A = 0.0335 m2.Part (a) Express the absolute pressure at the depth of h, P, in terms of P0, p and h.Part (b) Calculate the numerical value of P in PaPart (c) Express the magnitude of the force exerted by water on the top of the person’s head F at the depth h in terms of P and A.Part (d) Calculate the numerical value of F in N

FREE Expert Solution

Part (a)

Pressure increases with depth.

The pressure is directly proportional to depth, h.

The gauge pressure, Pg = hρg

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Problem Details

A person is diving in a lake in the depth of h = 9.5 m. The density of the water is ρ = 1.0×103 kg/m3. The pressure of the atmosphere is P0 = 1.0×105 Pa. The surface area of the top of the person’s head is A = 0.0335 m2.

Part (a) Express the absolute pressure at the depth of h, P, in terms of P0, p and h.

Part (b) Calculate the numerical value of P in Pa

Part (c) Express the magnitude of the force exerted by water on the top of the person’s head F at the depth h in terms of P and A.

Part (d) Calculate the numerical value of F in N

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