8.3 Challenging Integral Applications
Physics & Engineering Applications
Question #2 (Medium): Hydrostatic Force on a Submerged Vertical Plate
The hydrostatic force is given by ∑ ∫ , where is the water density,
the depth below the surface, the area of the thin th strip.
A vertical plate that is submerged in water has the shape shown by the diagram. Express the hydrostatic
force against one side of the place by a Riemann sum as well as an integral, and then evaluate it.
[a semi-circle with diameter ometer submerged meter deep]
Since the units are given in the Standard International metric system, ( )
As for the th rectangular strip, the area. If any th strip is chosen to be x distance from the
bottom of the semi-circle, then based on Pythagorean Theorem, the width (or even length) is:
√ ( ) . The distance the th strip is located beneath