Hydrostatic force practice problems
Force of water on a submerged vertical plate: pressure grows with depth, so integrate over strips. 10 problems with worked solutions; in 10 of them every equation is proved by a computer algebra system.
A vertical plate shaped like a semicircle of radius 3 m, flat side up is submerged in water with its top at the surface. Find the force of the water on one side. (Water weighs \( \displaystyle 9800\ \text{N}/\text{m}^3 \).)
A vertical plate shaped like a triangle with a 6-ft horizontal top edge and its vertex 4 ft below that edge is submerged in water with its top 2 ft below the surface. Find the force of the water on one side. (Water weighs \( \displaystyle \frac{312}{5}\ \text{lb}/\text{ft}^3 \).)
A vertical plate shaped like a rectangle 4 ft wide and 3 ft tall is submerged in water with its top at the surface. Find the force of the water on one side. (Water weighs \( \displaystyle \frac{312}{5}\ \text{lb}/\text{ft}^3 \).)
A vertical plate shaped like a triangle with a 4-ft horizontal top edge and its vertex 3 ft below that edge is submerged in water with its top 2 ft below the surface. Find the force of the water on one side. (Water weighs \( \displaystyle \frac{312}{5}\ \text{lb}/\text{ft}^3 \).)
A vertical plate shaped like a triangle with a 3-m horizontal top edge and its vertex 4 m below that edge is submerged in water with its top 1 m below the surface. Find the force of the water on one side. (Water weighs \( \displaystyle 9800\ \text{N}/\text{m}^3 \).)
A vertical plate shaped like a triangle with its vertex at the top and a 4-m horizontal base 3 m below the vertex is submerged in water with its top 2 m below the surface. Find the force of the water on one side. (Water weighs \( \displaystyle 9800\ \text{N}/\text{m}^3 \).)
A vertical plate shaped like a triangle with a 5-m horizontal top edge and its vertex 4 m below that edge is submerged in water with its top 2 m below the surface. Find the force of the water on one side. (Water weighs \( \displaystyle 9800\ \text{N}/\text{m}^3 \).)
A vertical plate shaped like a triangle with its vertex at the top and a 2-ft horizontal base 3 ft below the vertex is submerged in water with its top at the surface. Find the force of the water on one side. (Water weighs \( \displaystyle \frac{312}{5}\ \text{lb}/\text{ft}^3 \).)
A vertical plate shaped like a rectangle 4 ft wide and 4 ft tall is submerged in water with its top at the surface. Find the force of the water on one side. (Water weighs \( \displaystyle \frac{312}{5}\ \text{lb}/\text{ft}^3 \).)
A vertical plate shaped like a triangle with its vertex at the top and a 5-m horizontal base 1 m below the vertex is submerged in water with its top 1 m below the surface. Find the force of the water on one side. (Water weighs \( \displaystyle 9800\ \text{N}/\text{m}^3 \).)