Hydraulics and Fluid Mechanics in ME
A hemispherical tank of radius (R) has an orifice of cross-sectional area (a) at its bottom and is full of liquid. The time required to empty the tank completely is

14π R7/2/15Cd × a √(2g)
14π R1/2/15Cd × a √(2g)
14π R3/2/15Cd × a √(2g)
14π R5/2/15Cd × a √(2g)

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Hydraulics and Fluid Mechanics in ME
The discharge through a large rectangular orifice is given by (where H1 = Height of the liquid above the top of the orifice, H2 = Height of the liquid above the bottom of the orifice, b = Breadth of the orifice, and Cd = Coefficient of discharge)

Q = (2/3) Cd × b × √(2g) × (H23/2 - H13/2)
Q = (2/3) Cd × b × √(2g) × (H22 - H12)
Q = (2/3) Cd × b × √(2g) × (H21/2 - H11/2)
Q = (2/3) Cd × b × √(2g) × (H2 - H1)

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