1. Lesson 7.7 Fluid Pressure & Fluid Force

2. Definition of Fluid Pressure The pressure on an object submerged in a fluid is its weight- density times the height (depth) submerged: P = wh Common Weight-Densities (also in text):

3. We would like to calculate the entire force on an object in a fluid: The force would simply be the product of pressure and Area. F = PA(where P = wh) orF = whA Interesting fact: the force on a submerged object is the same from all directions. Units would be in pounds or kilograms right?

4. Example Find the fluid force on a rectangular sheet of metal (assume no thickness) submerged in water horizontally as shown below 5616 pounds Answer

5. So where’s the calculus? In the previous problem had 2 non-calculus assumptions: 1) Horizontal sheet: constant depth → constant pressure 2) The rectangular sheet stayed the same size Both assumptions can change in terms of the height (y variable) For example, take a spherical disk submerged vertically: Here: 1)Rectangular sheets would have different pressure at different depths (heights) 2)The length of the sheet would change, and 3)We have to take the thickness into account

6. So for a vertically submerged plane: Integrate infinitely small, horizontal rectangles Dimensions will change so we have changes in our variables

7. Example A square, vertical gate for a dam has sides 2 meters as shown below. Find the fluid force on the gate (density = 1000 kg/m 3 ). 9656.85 kg Answer