n open rectangular tank is filled to a depth of 2 m with water (density 1000 kg/m3). On top of the water there is a 1 m deep layer of gasoline (density 700 kg/m3). The width of the tank is 1 m (the direction perpendicular to the paper). The tank is surrounded by air at atmospheric pressure. Calculate the total force on the right wall of the tank, and specify its direction. The acceleration of gravity g = 9.81 m/s2.

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Physics

Braeden Fleming

Today, 12:56

n open rectangular tank is filled to a depth of 2 m with water (density 1000 kg/m3). On top of the water there is a 1 m deep layer of gasoline (density 700 kg/m3). The width of the tank is 1 m (the direction perpendicular to the paper). The tank is surrounded by air at atmospheric pressure. Calculate the total force on the right wall of the tank, and specify its direction. The acceleration of gravity g = 9.81 m/s2.

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Tyree · Answer 1

gasoline zone P_net = 6860 Pa

Water zone P_net = 26460 Pa

Force direction is out of tank

Explanation:

The pressure is defined

P = F / A

F = P A

let's write Newton's equation of force

F_net = F_int - F_ext

P_net A = (P_int - P_ext) A

The P_ext is the atmospheric pressure

P_ext = P₀

the pressure inside is

gasoline zone

P_int = P₀ + ρ' g h'

water zone

P_int = P₀ + ρ' g h' + ρ_water h_water

we substitute

Zone with gasoline

P_net = ρ' g h'

P_net = 700 9.8 1

P_net = 6860 Pa

Water zone

P_net = rho' g h' + rho_water g h_water

P_net = 6860 + 1000 9.8 2

P_net = 26460 Pa

To find the explicit value of the force, divide by a specific area.

Force direction is out of tank