6. Properties of Areas

Try these first

1. 1.

   What is the formula for calculating the resultant force on a horizontal plane area submerged in a fluid?

   Hint

   Consider how pressure is affected by depth.

2. 2.

   Where does the resultant force act on a plane surface?

   Hint

   Think about where pressure is best represented.

3. 3.

   What is the resultant force on a submerged surface directly proportional to?

   • Area
   • Depth
   • Both Area and Depth

   Hint

   Recall how pressure is affected by both these factors.

4. 4.

   True or False: The center of pressure is always at the centroid.

   • True
   • False

   Hint

   Consider how pressure acts differently at various points.

5. 5.

   A triangular plate with a base of 2 m and height of 3 m is submerged at an angle. Calculate the resultant force acting on it and determine the location of the center of pressure.

   Hint

   Approach by breaking down the height increments.

6. 6.

   You have a circular gate submerged in water at a depth of 5 m. Calculate the total force acting on the gate as well as the center of pressure. Dimensions of the gate are radius 1 m.

   Hint

   Think about how the circle simplifies the integration for circular sections.