Ying Yi PhD Chapter 11 Fluids 1 PHYS HCC

Outline PHYS HCC 2 Density and Pressure Pressure and Depth in a Static fluid Buoyant Forces and Archimedes’ Principle Fluids in Motion: Continuity Equation

Density The density of a substance of uniform composition is defined as its mass per unit volume: Units are kg/m 3 (SI) or g/cm 3 (cgs) 1 g/cm 3 = 1000 kg/m 3 3 PHYS HCC

Pressure (General) PHYS HCC 4

Which one would you pick to walk across snow? PHYS HCC 5 Why?

PHYS HCC 6 Pressure (Fluids) The force exerted by a fluid on a submerged object at any point is perpendicular to the surface of the object

Why need diving suit in deep sea? PHYS HCC 7

8 Measuring Pressure The spring is calibrated by a known force The force the fluid exerts on the piston is then measured

Example 11.2 The force on a swimmer PHYS HCC 9

Notes on Atmospheric Pressure PHYS HCC 10 Temperature: 20º Altitude: Sea level air density = kg/m³ Relative humidity: 20% Standard atmospheric Pressure: 1.01 × 10 5 Pa

Pressure Values in Various Units One atmosphere of pressure is defined as the pressure equivalent to a column of mercury exactly 0.76 m tall at 0 o C where g = m/s 2 One atmosphere (1 atm) = 76.0 cm of mercury × 10 5 Pa 14.7 lb/in 2 11 PHYS HCC

Pressure and Depth in a Static fluid PHYS HCC 12

Irregular shaped container PHYS HCC 13

Example 11.4 Swimming pool PHYS HCC 14 Figure 11.7 shows the cross section of a swimming hole. Points A and B are both located at a distance of h=5.50m below the surface of the water. Find the pressure at each of these two points.

Group Problem: Blood Pressure PHYS HCC 15

Absolute vs. Gauge Pressure The pressure P is called the absolute pressure Remember, is the gauge pressure 16 PHYS HCC

Sphygmomanometer PHYS HCC 17

Pascal’s Principle A change in pressure applied to an enclosed fluid is transmitted undimished to every point of the fluid and to the walls of the container. First recognized by Blaise Pascal, a French scientist (1623 – 1662) 18 PHYS HCC

19 Pascal’s Principle, cont The hydraulic press is an important application of Pascal’s Principle

Example 11.7 A Hydraulic Car Lift PHYS HCC 20

Group Problem: Car Lift PHYS HCC 21

PHYS HCC 22 Archimedes 287 – 212 BC Greek mathematician, physicist, and engineer Buoyant force Inventor

Archimedes' Principle Any object completely or partially submerged in a fluid is buoyed up by a force whose magnitude is equal to the weight of the fluid displaced by the object 23 PHYS HCC

24 Buoyant Force The upward force is called the buoyant force The physical cause of the buoyant force is the pressure difference between the top and the bottom of the object

Buoyant Force, cont. The magnitude of the buoyant force always equals the weight of the displaced fluid The buoyant force is the same for a totally submerged object of any size, shape, or density 25 PHYS HCC

Buoyant Force, final The buoyant force is exerted by the fluid Whether an object sinks or floats depends on the relationship between the buoyant force and the weight 26 PHYS HCC

Totally Submerged Object The upward buoyant force is B= ρ fluid gV obj The downward gravitational force is W=mg= ρ obj gV obj The net force is B-W=( ρ fluid - ρ obj )gV obj 27 PHYS HCC

Floating Object The object is in static equilibrium The upward buoyant force is balanced by the downward force of gravity Volume of the fluid displaced corresponds to the volume of the object beneath the fluid level 28 PHYS HCC

Example 11.9 A swimming Raft PHYS HCC 29 A solid, square pinewood raft measures 4.0 m on a side and is 0.30 thick. (a) Determine whether the raft floats in water, and (b) if so, how much of the raft is beneath the surface (see the distance h in Figure 11.18).

Group Example: submerged object PHYS HCC 30 A bargain hunter purchases a “gold” crown at a flea market. After she gets home, she hangs it from a scale and finds its weight to be 7.84 N (Fig. 9.24a). She then weighs the crown while it is immersed in water, as in Figure, and now the scale reads 6.86 N. Is the crown made of pure gold?

Fluids in Motion: Equation of Continuity PHYS HCC 31

Equation of Continuity PHYS HCC 32

Application: Garden Hose PHYS HCC 33 Why would the speed of water change?

Group Example: A Garden Hose PHYS HCC 34

Homework 2, 7, 13, 23, 25, 37, 43,45, 51, 56 PHYS HCC 35 Happy Thanksgiving!