In the Netherlands, a dike holds back the sea from a town below sea level The dike springs a leak 4.0 m below the water surface. If the area of the hole in the dike is 1.0 cm2, what force must the Dutch boy exert to save the town?
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In the Netherlands, a dike holds back the sea from a town below sea level The dike springs a leak 4.0 m below the water surface. If the area of the hole in the dike is 1.0 cm2, what force
Pressure = Density * g * depth
The pressure of the water is directly proportional to the depth.
AND
Pressure = Force ÷ area
The pressure of the water is inversely proportional to the area.
SO
Force ÷ area = Density * g * depth
Force = area * Density * g * depth
Newton = m^2 * kg/m^3 * m/s^2 * m
Newton = kg * m/s^2 OK, the units agree
Area in m^2 = 0.01^2
Density 1000 kg/m^3
g = 9.8 m/s^2
Force = 0.01^2 * 1000 * 9.8 * 4.0
Pressure = Density * g * depth
The pressure of the water is directly proportional to the depth.
AND
Pressure = Force ÷ area
The pressure of the water is inversely proportional to the area.
SO
Force ÷ area = Density * g * depth
Force = area * Density * g * depth
Newton = m^2 * kg/m^3 * m/s^2 * m
Newton = kg * m/s^2 OK, the units agree
Area in m^2 = 0.01^2
Density 1000 kg/m^3
g = 9.8 m/s^2
Force = 0.01^2 * 1000 * 9.8 * 4.0