1. ES 202 Fluid and Thermal Systems Lecture 4: Pressure Distributions on Submerged Surface (12/09/2002)

2. Assignments Reading: –Mechanics: definition of center of mass, moment of inertia –Cengel & Turner Section 5-4 –ES 201 notes Homework: –10-11, 10-19, 10-37 in Cengel & Turner

3. Road Map of Lecture 4 Announcements Examples and exercises (from first principle to generalization) –Force and moment on vertically submerged surface Concept of resultant force, centroid and center of pressure F R = P avg * A where P avg is measured at the centroid of the submerged surface Center of pressure is located lower than the centroid according to y p = y c + I xx,c / y c A where y c is the location of centroid and I xx,c / y c A is the downward shift of center of pressure relative to centroid –Force and moment on obliquely submerged surface –Force and moment on curved surface Horizontal component is the same Vertical component is different according to the weight of fluid that is above surface

4. Announcements First homework set due by 5 pm today at my office

5. Quiz on Lecture 3 When a fluid is in static equilibrium, –the hydrostatic pressure increases/decreases ____________ with depth; –the pressure gradient (rate of change) depends on the ____________ of the fluid. Something about manometer: –A manometer is a device which measure small pressure difference based on the difference in ____________ between fluid columns –For a given pressure difference, the difference in height between the fluid columns will be greater if a fluid of lower/higher density is used. –The pressure equation: P 2 = P 1 +/-  g h describes the pressure variation in a manometer. The minus (-) sign is used when Point 2 lies above/below Point 1 and vice versa.

6. Vertically Submerged Surface Fish tank problem –What is the pressure at the bottom of the tank? –Sketch the pressure distribution on the side wall? –Find the total force on one of the side walls –Find the total moment on the side wall about Point A –Find the center of pressure (take a first guess at its approximate location)

7. Obliquely Submerged Surface Same old fish tank problem If one of the sides of the fish tank is slightly sloped at 30 o, how will the followings be different? –Analysis –Results (take a first guess before you work out the details)

8. Curved Surface Same old fish tank problem If the slope is replaced by a –concave surface –convex surface What do you expect the results to be?