# Example Problem with Complete Solution

1B-6 : Force Required to Lift an Underwater Gate 5 pts
A steel plate rests on the horizontal bottom of a water tank that is 3 m deep. What upward force, in N, must be applied to the steel plate to just barely lift it straight upward? The plate is 20 cm in diameter.
Assume the weight of the plate is negligible.

Read: The key to this problem is to recognize that the TOTAL force required to just barely lift the man-hole cover is equal to the force exerted on the top surface of the man-hole cover by both the atmosphere and the water.  This force is equal to the absolute pressure at the bottom of the tank times the area of the man-hole cover.  The force a man or machine would need to exert in order to lift the man-hole cover is less because atmospheric pressure is also acting on the outer or bottom surface of the man-hole cover.
Given: D 0.2 m gc 1 kg-m/N-s2
h 3 m
Find: Fup ??? kN
Assumptions: 1- Assume: g 9.8066 m/s2
Patm 100 kPa
rH2O 1000 kg/m3
Equations / Data / Solve:
The total force required to just barely lift the man-hole cover is: Eqn 1
The gate is circular, so : Eqn 2
Plug values into Eqn 2 : Agate 0.03142 m2
Next, we can use the Barometer Equation to determine the pressure at the bottom of the tank. Eqn 3
Pbottom 129.4 kPa
Finally, we substitute values into Eqn 1 to answer the question : F 4066 N
This is the total force required to lift the man-hole cover.  But atmospheric pressure is also acting on the outside or bottom surface of the manhole cover as well.  So, since we want to determine how much additional force must be applied in order to lift the man-hole cover, we must subtract the upward force attributable to atmospheric pressure below the cover. Eqn 4
Fatm 3142 N
The additional force that must be exerted to lift the man-hole cover is the difference between the total force required and the force exerted by the atmosphere. Eqn 5 Fup 924.3 N
If the door had a hinge, the problem would be a bit more challenging because it would involve the computation of torques acting around the axis of the hinge.  Torques and lever arms are not part of this thermodynamics course. 