Hydrostatic Force on a Plane Surface-8 (3)

Hydrostatic Force on a Plane Surface Purpose: To verify the theoretical prediction of the resultant hydrostatic force and its point of action on both (a) partially submerged and (b) fully submerged plane surface in a liquid. Apparatus: Armfield Hydrostatic Force Demonstration Unit

Theory: (Ref. Munson/Young/Okiishi  A Brief Introduction to Fluid Fluid Mechanics, p.46-53 & p.69)

Review the derivation of the resultant magnitude and point of action of hydrostatic force on a submerged plane surface. List these expressions for a vertical surface that is (a) partially submerged, and (b) fully submerged. Sketch a free-body diagram for the quarter-circle block assembly, and prove the following expressions for the moment about the pivot point (O) exerted by the hydrostatic force.

ℎ<  = 2 ℎ ( − ℎ3) ℎ>    =(ℎ− 2 )  − 2 + 12ℎ−6

(a) When the surface is partially submerged

(b) When the surface is fully submerged



where  is the specific weight

=

:

:

 of the fluid.

Explain why the hydrostatic pressures on the two curved surfaces have no effect on the resultant moment.

Procedure: 1. With no water in the tank and no weights in the weighing pan, adjust the position of the counter weight so that the horizontal arm is balanced about the pivot point. 2. Add water to the tank so that the plane surface is submerged to a depth of about 1 cm. 3. Add weights to the pan until the arm is balanced again. Record the weights. 4. Add more water to the tank so that the water depth is increase by about 1 cm. 5. Repeat steps 3 and 4 until the maximum reading for water depth on the surface is reached. 6. The next squad of students now takes over and reverses the procedure by draining water so that the depth decreases by about 1 cm at a time. Results: 1. For each , compute the hydrostatic force on the plane surface, its point of action  below the water surface, and the resultant moment about the pivot point of the block. Provide sample calculations for both the (a) partially submerged and (b) fully submerged cases. 2. Compute the moment about the pivot point exerted by the weights to balance the block. 3. Plot the theoretical moment due to the hydrostatic force and the experimental moment balanced by the weights versus h on the same chart for comparison.

ℎ

ℎ

Conclusion: Conclude if the theoretical prediction of the magnitude and point of action of the hydrostatic force on a plane surface is verified.

Date: _____________

Data:





Width  & Height of Surface: Radii of Curved Surfaces: Moment Arm Length of Balancing W eights: Water Depth

ℎ 

 ==7.104   ==1020 = 27.5     ℎ 

Balancing Mass

Water Depth

Balancing Mass

 