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8 November, 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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  1. 8 November, 14:29
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    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
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