a tank is 10 m long, 4 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.

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21-10-2022
Physics

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a tank is 10 m long, 4 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.

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kjuli1766 kjuli1766 · Answer 1 · 2022-10-25T07:28:17-04:00

The hydrostatic pressure on the bottom of the tank is 197.083 kN.

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. Hydrostatic pressure at the underside of the tank:

P = ρ g h

P = 820 x 9.81 x 3.5

P = 28154.7 Pa

B. Hydrostatic force at the underside of the tank:

F = P A

⇒A = 10 x 8 = 80 meter²

⇒F = 28154.7 x 80

= 2252.38 kN

C. Hydrostatic force at one edge:

Given,

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 = 24.5 ρg

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

The pressure exerted by a liquid thanks to gravity at any point in equilibrium. Hydrostatic pressure is proportional to the depth measured from the surface because the weight of the liquid increases when a downward force is applied. Hydrostatic pressure is the force produced by still or still water. this is often the constant force that water pressure exerts on underground walls.

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