Question

A person is diving in a lake in the depth of h = 5.5 m. The density of the water is rho = 1.0 x10^3 kg/m^3. The pressure of the atmosphere is P0 = 1.0 x 10^5 Pa. The surface area of the top of the person's head is A = 0.046 m^2.
(a) Express the absolute pressure at the depth of h, P, in terms of P0, rho, and h.
(b) Calculate the numerical value of P in Pa.
(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.
(d) Calculate the numerical value of F in N.

Answer 1

Answer:a) P = Po + rho×h×g

b) P = 5.4 × 10^9 pa

c) F = P/A = (Po + rho×h×g)/A

d) 1.174×10^11N

Explanation: Using the formula

P = Po + rho×h×g

P =  1.0 x 10^5 + 1000 × 5.5 × 9.81

P = 5.4 × 10^9pa

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

F = P/A = (Po + rho×h×g)/A

Using the above formula

Where A = 0.046m^2

F = P/ A = 5.4×10^9/0.046

F = 1.174×10^11N