An outlet of diameter 1 m is made 20 m below the surface of water in a dam. Determine the force with which the water spews out when it is fully opened due to water pressure (Take g = 10 N/Kg and density of water = 1g/cm³
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We know that the pressure below a water column of height h is ,
P = hρg where, h is the height of water column
ρ is the density of water column
g is the acceleration due to gravity
Here,
Height = h = 20m
Density = ρ = 1g/cm³ = 1000kg/m³
Acceleration due to gravity = g = 10N/kg = 10m/s²
Hence
P at the outlet = 20 * 1000 * 10
= 2×10⁵ Pa
We also know that,
Pressure = Force / Area
P = F/A
A = Area of the outlet = πd²/4 = 3.14 * 1/4 = 0.785 m²
Hence
Force = Pressure × Area
= 2×10⁵×0.785
= 1.57×10⁵ N
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