Understanding Density and Pressure in Fluids

2. Density

3. Densities of some common materials Density depends on the temperature and pressure when it is measured. These values are at 0C and atmospheric pressure.

4. Contact forces due to a fluid p A F

5. Poll You are under water in a swimming pool. The force of water on any part of the surface of your body is due to The weight of water Water currents Water pushing on your body Collisions of water molecules with your body

6. Units 1 atm = 760 mm Hg 1 atm = 1.01 x 105 Pa

7. Pressure as a function of depth

8. Gauge Pressure

9. Example The atmospheric pressure at the surface of Venus is about 90 times the Earth’s atmospheric pressure at its surface. How far below the sea level in the ocean would you have to go in order to find the same pressure as on the surface of Venus? Assume that seawater is incompressible (i.e. its density is uniform) and is a static fluid. The density of seawater at 20◦ C and a pressure of 1 atm is 1.024x103 kg/m3 .

10. Poll How far below the surface of water is the pressure two times the pressure at the surface? 1 m 2 m 10 m 20 m 100 m

13. Suppose we mentally isolate two cylindrical “chunks” of a larger body of water. The top and bottom surfaces of the two cylinders are numbered. Which of the following correctly compares the pressure on these four surfaces? D. P2 > P4 > P1 > P3 E. P2 > P1 > P4 > P3 A. P2 = P4 > P1 = P3 B. P1 = P3 > P2 = P4 C. P1 = P2 > P3 = P4 1 3 2 4

14. Suppose we mentally isolate two cylindrical “chunks” of a larger body of water. The top and bottom surfaces of the two cylinders are numbered. Which of the following correctly compares the pressure on these four surfaces? Suppose we now isolate the two cylindrical “chunks” a little bit differently – see below. Which of the following correctly compares the pressure on these four surfaces? D. P2 > P4 > P1 > P3 E. P2 > P1 > P4 > P3 A. P2 = P4 > P1 = P3 B. P1 = P3 > P2 = P4 C. P1 = P2 > P3 = P4 D. P2 > P4 > P1 > P3 E. P2 > P1 > P4 > P3 A. P2 = P4 > P1 = P3 B. P1 = P3 > P2 = P4 C. P1 = P2 > P3 = P4 3 1 1 3 4 2 2 4

15. Consider the containers at right. Which of the followingcorrectly compares how much pressure (P) the water exerts on the bottoms of the containers? A 2A A 2h h h A 1 2 3 D. P2 > P1 > P3 E. P1 = P2 > P3 A. P1 = P2 = P3 B. P3 > P1 > P2 C. P3 > P1 = P2

16. Consider the containers at right. Which of the followingcorrectly compares how much force (F) the water exerts on the bottoms of the containers? A 2A A 2h h h A 1 2 3 D. F2 > F3 > F1 E. F1 = F2 = F3 A. F2 > F1 > F3 B. F2 > F1 = F3 C. F3 > F1 > F2

17. Buoyant force

18. Archimedes’ Principle The buoyant force on a fluid on an object in the fluid is equal to the weight of the fluid displaced by the object.

19. Poll An object is held at rest under water. It is completely immersed. If it is moved to a greater depth, does the buoyant force on the object increase, decrease, or remain constant? Increase Decrease Remain constant

20. Poll A piece of Styrofoam is held under water. When it is released, it travels upwards until it floats. As it is rising upward, but still completely immersed in the water, is the buoyant force greater than, less than, or equal to the weight of the object? Greater than Less than Equal to

21. Poll A piece of Styrofoam is held under water. When it is released, it travels upwards until it floats. As it is rising above the surface, does the buoyant force on the Styrofoam increase, decrease, or remain constant. increase Decrease Remain constant

22. Poll What variables does the buoyant force of a fluid on an object depend on? Depth in the fluid Density of the fluid Mass of the object How much of the object is submerged All of the above 1 and 2 3 and 4 2 and 4

24. 1 2 3 The treasure chest is sinking from position 1 to position 2 to position 3 As it goes from position 1 to position 2, the buoyant force that the water exerts on it _______________. A. increases B. decreases C. remains the same

25. 1 2 3 The treasure chest is sinking from position 1 to position 2 to position 3 As it goes from position 2 to position 3, the buoyant force that the water exerts on it _______________. A. increases B. decreases C. remains the same

26. 1 2 3 4 The four blocks above are floating in water. They have the same horizontal dimensions (length and width) but different heights. They may also be made of different materials. Which of the following correctly compares the weights (w) of the blocks? D. w3> w4 > w2 > w1 E. w3 > w2 = w4 > w1 A. w3 = w4 > w1 = w2 B. w2 = w3 > w1 = w4 C. w1 = w2 = w3 = w4

27. Example What percentage of the volume of an ice cube floats above water? The density of ice is 0.97x103 kg/m3.

28. Poll The water level in a cup with ice is exactly at the edge of the top of the cup. After the ice melts, does the water level rise, fall, or remain the same? Rises Falls Remains the same

29. Example What is the buoyant force of air on a helium balloon? Assume that the balloon is a sphere of radius 10 cm. What should be the mass of string and latex for the balloon to float in air at equilibrium?

30. Example Suppose a 10-kg buoy has a volume of 1m3 . Suppose that you want the buoy to be suspended in water so that it neither rises to the top nor sinks to the bottom. How much water must be let into the buoy?