Fluids. P 2 = P 1 + ρgh P 2 P. = ρgh. Gauge pressure. (See revision to posted in previous lecture notes.) ccby Alex Anlicker

Transcription

1 Fluids P 2 = P 1 + ρgh P 2 P!# "# atm $ = ρgh Gauge pressure (See revision to posted in previous lecture notes.) ccby Alex Anlicker

2 C&J An object is solid throughout. When the object is completely submerged in ethyl alcohol, its apparent weight is 15.2 N. When completely submerged in water, its apparent weight is 13.7 N. What is the volume of the object?

3 Steady Flow Making streamlines with dye and smoke.

4 The equation of continuity For steady flow. Mass flow rate: the mass of fluid per second that flows through a tube.

5 Mass that flows past a point on the tube in time t : Δm = ρδv = ρavδt 2) Since V = Area * l Δm Δt 1) Since v = length/time àl = v* Δt.

6 Tube which narrows at some point: Mass flow rate at two points: Δm 2 Δt SI unit: kg/s = ρ 2 A 2 v 2 Δm 1 Δt = ρ 1 A 1 v 1

7 Continuity: The mass flow rate is the same at every position along a tube that has a single exit and entrance. What goes in must come out. Equation of continuity ρ 1 A 1 v 1 = ρ 2 A 2 v 2 If the fluid is incompressible ρ 1 = ρ 2 A 1 v 1 = A 2 v 2 If cross-sectional area decreases, velocity increases.

8 i>clicker A faucet is left open. The diameter of the stream is 0.25d at the bottom and d at the top as it falls from the faucet. The explanation for this narrowing of the stream is: a) Atmospheric pressure is greater than the pressure within the stream of water. b) The water has left the pipe that carried it and no longer maintains the shape of the pipe. c) The water accelerates as it falls and the crosssectional area must decrease to maintain a constant flow rate. d) The flow rate at the top of the stream is not sufficient to maintain a constant cross-sectional area.

9 Conservation of mechanical energy in fluid flow Bernoulli s equation V F1 F2 V

10 V F1 x1 F2 V x2 And m/v = density.

11 For the 2 positions this becomes: (P 2 P 1 )+ 1 2 v v2 1 +( gh 2 gh 1 )=0 Re-arrange so that each position is on one side of the equal sign.

12 BERNOULLI S EQUATION In steady flow of an ideal fluid, the pressure, the fluid speed, and the elevation at two points are related by: P ρv 1 2 +ρgh 1 = P ρv 2 2 +ρgh 2 note: This equation was derived for incompressible fluids only, but it is also true that for gases the pressure drops where the speed is faster.

13 i>clicker Fluid is flowing from left to right thru the pipe shown. A & B are at the same height, but the cross-sectional areas of the pipe are different at these 2 locations. B & C are at two different heights, but have the same crosssectional areas. Rank the pressures at the 3 locations in order from lowest to highest? a) P A > P B > P C b) P A > P B = P C c) P C > P B > P A d) P B > P A and P B > P C e) P C > P A and P C > P B

14 Applications of Bernoulli s equation The airplane wing Image reprinted with permission of John Wiley and Sons, Inc.

15 Torricelli s Law A tank has a hole in its side. Determine the speed with which the liquid leaves the tank. P 1 = P 2, assume that the tank is large so that the liquid level changes slowly and v 2 = 0. 0 P ρv 1 2 +ρgh 1 = P ρv 2 2 +ρgh ρv 1 2 +ρgh 1 = ρgh 2 v 1 = 2g( h 2 h 1 ) P 1

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20 Heat and Temperature Temperature scales 1C! = 9 5 F! Convert from degrees F to degrees C: T C = T F 32 ( ) 5 9

21 The Kelvin Temperature Scale Temperature scale scientists use. One kelvin equals one Celsius degree.

22 Constant volume gas thermometer Ideal gas PV = nrt Constant volume: P = (constant)t

23 Measure known temperatures and plot vs. pressure. For all gases, a straight line fit crosses zero P at T = C.

24 Linear Thermal Expansion Normal solids Image reprinted with permission of John Wiley and Sons, Inc. Solids expand in volume when T is raised because inter-atomic spacing becomes larger.

25 The change in any linear dimension (length, width or depth), ΔL, that is proportional to L is called the linear thermal expansion. Unit: 1/ C (prefer 1/k) Image reprinted with permission of John Wiley and Sons, Inc.

26 i>clicker A rod of length L is heated so that its temperature increases by ΔT. As a result, the length of the rod increases by ΔL. The rod is then cut into two pieces, one of length L/3 and one of length 2L/3. What is the ratio of the change in length of the rod of length 2L/3 to ΔL of the original rod when its temperature is increased by ΔT? a) 2/3 b) 1 c) 3/2

27 Homework Read 11.10, 12.1, 12.2, 12.3, 12.4 (excluding thermal stress). Read ahead the rest of Chapter12. C&J WileyPlus assignment 9 due Tuesday at 12:15 pm, WileyPlus assignment 10 available Friday and due Jan. 4, 2017 at 12:15pm Assignment solutions are available online right after the deadline. Exam Jan 16, 2017 at 3:30 PM in FR Kennedy Brown Gym