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13 May, 19:05

A rectangular trough, 1.5 m long, 0.50 m wide, and 0.40 m deep, is completely full of water. One end of the trough has a small drain plug right at the bottom edge. Part APart complete When you pull the plug, at what speed does water emerge from the hole

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  1. 13 May, 19:29
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    V = 2.801 m/s

    Explanation:

    Given.

    - The dimension of the tank = 1.5 x 0.5 x 0.4 m

    - A plug at the bottom of the tank

    Find:

    When you pull the plug, at what speed does water emerge from the hole

    Solution:

    - We can compute the solution either by an energy balance or Bernoulli's equation as follows:

    P_1 + 0.5*p*V_1^2 + p*g*z_1 = P_2 + 0.5*p*V_2^2 + p*g*z_2

    Where,

    P: Pressure of the fluid (gauge)

    V: Velocity of the fluid

    p: Density of the fluid

    z: The elevation of fluid from datum (free surface)

    g: The gravitational acceleration constant

    - We will consider the two states by setting a datum at the bottom of the surface.

    State 1 (Free surface of the fluid at level):

    P_1 = 0 (gauge - atm)

    V_1 = 0 (Free surface)

    z_1 = 0.40 m

    State 2 (Plug level @ bottom):

    P_2 = 0 (gauge - atm)

    V_2 = unknown (need to calculate)

    z_1 = 0 ... (datum)

    - Lets plug the values at each state in the equation above:

    0 + 0 + p*g*z_1 = 0 + 0.5*p*V_2^2 + 0

    V^2 = 2*g*z_1

    V = sqrt (2*g*z_1)

    V = sqrt (2*9.81*0.4)

    V = 2.801 m/s
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