Question

A tank is 10 m long, 8 m wide, 4 m high, and contains kerosene with density 820 kg/m3 to a depth of 3.5 m. (Use 9.8 m/s2 for the acceleration due to gravity.) (a) Find the hydrostatic pressure on the bottom of the tank. Pa (b) Find the hydrostatic force on the bottom of the tank. N (c) Find the hydrostatic force on one end of the tank. N

Answer 1

The hydrostatic pressure on the bottom of the tank is 27,790 Pa. The hydrostatic force on the bottom of the tank is 2,223,200 N. The hydrostatic force on one end of the tank is 889,600 N.

Step-by-step explanation:

To find the hydrostatic pressure on the bottom of the tank, we can use the formula:

pressure = density x gravity x height

where density is 820 kg/m^3, gravity is 9.8 m/s^2, and height is 3.5 m. Plugging in these values, we get:

(a) pressure = 820 kg/m^3 x 9.8 m/s^2 x 3.5 m = 27,790 Pa

To find the hydrostatic force on the bottom of the tank, we can use the formula:

force = pressure x area

where area is the length times the width of the tank. Plugging in the values, we get:

(b) force = 27,790 Pa x (10 m x 8 m) = 2,223,200 N

To find the hydrostatic force on one end of the tank, we can use the formula:

force = pressure x area

where area is the width times the height of the tank. Plugging in the values, we get:

(c) force = 27,790 Pa x (8 m x 4 m) = 889,600 N

Answer 2

Given,

Length of tank = 10 m

Width of tank = 8 m

height of tank = 4 m

density of kerosene = 820 kg/m³

depth of oil = 3.5 m

a) Hydro static pressure at the bottom of the tank

P = ρ g h

P = 820 x 9.81 x 3.5

P = 28154.7 Pa

b) Hydrostatic force at the bottom of the tank

F = P A

A = 10 x 8 = 80 m²

F = 28154.7 x 80 = 2252.38 kN

c) Hydrostatic force at one edge

Width = 8 m

depth = z

A = 4 y

dA = 4 dy

P = ρgh

P = ρgz = ρg(y-0.5)

F = P dA

F = ρg(y-0.5)(4dA)

`F = 4\rho g \int_(0.5)^4(y-0.5)dy`

on solving

F = 24.5 ρg

Hydrostatic force at one end = 24.5 x 820 x 9.81 = 197.083 kN.