3. Resultant Forces and Centroid

Try these first

1. 1.

   Define resultant force in the context of fluid statics.

   Hint

   Think about the relationship between pressure and area.

2. 2.

   What is the formula for pressure at depth?

   Hint

   Consider what happens as you go deeper into a fluid.

3. 3.

   What is the formula for resultant force on a plane area?

   • F_R = PA
   • F_R = ρghA
   • F_R = ργA

   Hint

   Review the relationship between pressure and area.

4. 4.

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

   • True
   • False

   Hint

   Remember how pressure changes with depth.

5. 5.

   A submerged triangular surface has a base of 4m and height of 3m. Calculate the resultant force if submerged to a depth of 6m in water (γ = 9.81 kN/m³).

   Hint

   Break it down into steps: calculate area first, then centroid, and finally resultant force using the formula.

6. 6.

   You have a circular gate of diameter 2m submerged in water up to a depth of 4m. Find the position of the center of pressure.

   Hint

   Remember to convert the diameter to radius and apply the correct formula for circular areas.