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

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)

on solving

 F = 24.5 ρg

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

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