Question

A person is diving in a lake in the depth of h = 9.5 m. The density of the water is rho = 1.0 x103 kg/m3. The pressure of the atmosphere is P0 = 1.0 x 105 Pa. The surface area of the top of the person's head is A = 0.0435 m2.Randomized Variables
h = 7.5 m
A = 0.0385 m2
Part (a) Express the absolute pressure at the depth of h, P, in terms of P0, ?, and h.
Part (b) Calculate the numerical value of P in Pa. P =
Part (c) Express the magnitude of the force exerted by water on the person's head F at the depth h in terms of P and A. 25% Part (d) Calculate the numerical value of F in N.

Answer 1

To solve the problem, it is necessary to apply the concepts related to pressure depending on the force and area, as well as the absolute pressure given by the laws of hydrostatics.

PART A) By definition and hydrostatic theory we know that the pascal principle defines pressure as,

$P = P_0 + \rho gh$

Where,

$P_0 =$Pressure at the top of the fluid column

P = Pressure at the bottom

$\rho$ = Density of fluid

G = Gravitational acceleration

h = Height

PART B) With the data previously given (taking the height as 9.5) we have to

$P = (1*10^5Pa)+(1000kg/m^3)(9.81m/s^2)(9.5m)$

$P = 1.93195*10^{5}Pa$

PART C) Pressure is defined as the force performed in a specific area, that is

$P = \frac{F}{A}$

Re-arrange to F, we have

$F=PA$

PART D) With the previous formula we proceed to calculate the force replacing the values, that is,

$F= PA$

$F = (1.93195*10^{5})(0.0385)$

$F = 7438N$