PHYSICS 0 Evening Exam Lecture 18 Fluid Dynamics The second exam is on Tuesday November Time 8:00-9:00 PM in three rooms depending on your lab section Phys 114 WTHR 00 EE 19 went to CL50 4 last time Closed book but one 8 1/ X 11 crib sheet allowed Bring calculator, # pencil, I.D. card Covers Chapters 6-10 Chapt. 6 is included Lecture 17 Purdue University, Physics 0 1 Locations by Lab Instructor WTHR 00 - Mandal, Nirajan Lin, Tzu-Ging Jung, Yookyung EE 19 - PHYS 114 -- Cervantes, Mayra Mukundan, Vineetha Li, Xin-A Setty, Chandan Shao, Siyi Zhang, Shunyuan See Home Page For lab hours Pressure in an oil well W is water O is oil P Oil = P A +! W h W +! R h R If column drilled filled with water P 1 = P A +! W h W +! W h R Oil will rise up tube and leak -- "P = (! R -! O )gh R R is rock If tube filled with mud heavier than! R P 1 > P O Can t force mud down from top unless pressure can be contained
Archimedes Principle Buoyant Force F B Weight of fluid displaced F B =! fluid V disp g F g = mg =! object V object g Object sinks if! object >! fluid Object floats if! object <! fluid If object floats F B = F g Therefore! fluid V disp g =! object V object g Therefore V disp / V object =! object /! fluid Exercise Suppose you float a large ice-cube in a glass of water, and that after you place the ice in the glass the level of the water is at the very brim. When the ice melts, the level of the water in the glass will: A) Go up, causing the water to spill out of the glass B) Go down C) Stay the same CORRECT W ice = F B =! W g V displaced W water =! W g V water W ice = W water V displaced = V water Lecture 17 Purdue University, Physics 0 5 Lecture 17 Purdue University, Physics 0 6 Exercise Which weighs more: A) A large bathtub filled to the brim with water B) A large bathtub filled to the brim with water with a toy battle-ship floating in it C) They weigh the same CORRECT Tub of water + ship Fluid Flow Concepts Weight of ship = Buoyant force = Weight of displaced water Tub of water Volume flow rate: "V/"t = Av (m 3 /s) Mass flow rate: "m/"t =!Av (kg/s) Overflowed water Lecture 17 Purdue University, Physics 0 7 Continuity:!A 1 v 1 =!A v mass flow rate the same everywhere Lecture 17 Purdue University, Physics 0 8
Faucet A stream of water gets narrower as it falls from a faucet (try it & see). Explain this phenomenon using the equation of continuity. V 1 A 1 Demo C - 01 A V From the continuity equation, we know that A 1 V 1 =A V. Therefore, as the velocity increases, the crosssectional area has to decrease. Since the water is in free fall gravity causes the speed to increase as it goes down. Because the speed is increasing the cross sectional area has to decrease in order to keep the product of the two equal. Lecture 17 Purdue University, Physics 0 9 Flow Speed and Pressure Continuity Equation says fluid speeds up going to smaller opening, slows down going to larger opening Acceleration due to change in pressure: P 1 > P Smaller tube has FASTER flow and LOWER pressure Bernoulli s Equation Consider tube where both area and height change W = "K + "U W = Fx = F/A Ax = PV (P 1 -P ) V =! m (v v 1 ) + mg(y -y 1 ) (P 1 -P ) V =!!V (v v 1 ) +!Vg(y -y 1 ) Where the velocity is high, the pressure is low and where the velocity is low the pressure is high Lecture 17 Purdue University, Physics 0 11 P 1 +!gy 1 +!!v 1 = P +!gy +!!v Tube wall doesn t move does no work Lecture 17 Purdue University, Physics 0 1
Dynamics of Ideal Fluids Conservation of mass # Continuity equation Volume Flow rate : Av = constant The same volume of fluid passes per unit time Conservation of energy # Bernoulli s equation Question What will happen when I blow air between the two plates? A) Move Apart B) Come Together C) Nothing P + 1!v +!gy = constant which relates height, velocity and pressure of the fluid There is air pushing on both sides of plates. If we get the air in the middle to move faster, then slower moving air on the outside has more pressure pushing them together. Lecture 17 Purdue University, Physics 0 13 Lecture 17 Purdue University, Physics 0 14 Demo C - 06 Question not why ball held up but why it doesn t fall out of stream Exercise Through which hole will the water come out fastest? P 1 +!gy 1 +!!v 1 = P +!gy +!!v A If ball leaves stream it has moving air on the stream side and stationary air outside Net pressure back into stream Note: All three holes have same pressure P=1 Atmosphere!gy 1 +!!v 1 =!gy +!!v gy 1 +! v 1 = gy +!v Smaller y gives larger v. Hole C is fastest B C Lecture 17 Purdue University, Physics 0 16
Problem A large bucket full of water has two drains. One is a hole in the side of the bucket at the bottom, and the other is a pipe coming out of the bucket near the top, which bent is downward such that the bottom of this pipe even with the other hole, like in the picture below: Through which drain is the water spraying out with a larger speed? A) The hole B) Same C) The pipe The speed of the water depends on the pressure at the opening through which the water flows, and on the depth of the opening from the surface of the water. Since both the hole and the opening of the downspout are at [the same] depth below the surface, water from the two will be discharged with the same speeds. Lecture 17 Purdue University, Physics 0 17 Example A garden hose with inner diameter cm, carries water at.0 m/s. To spray your friend, you place your thumb over the nozzle giving an effective opening diameter of 0.5 cm. What is the speed of the water exiting the hose? What is the pressure difference between inside the hose and outside? Continuity Equation A 1 v 1 = A v v = v 1 ( A 1 /A ) = v 1 ( r 1 / r ) = m/s x 16 = 3 m/s Bernoulli Equation P 1 +!gy 1 +!!v 1 = P +!gy +!!v P 1 P =!! (v v 1 ) =! x (1000 kg/m 3 ) (104-4 m /s ) = 5.1x10 5 Pa Lecture 17 Purdue University, Physics 0 18 Lift a House Calculate the lift force on a 15 m x 15 m house when a 30 m/s wind (1.9 kg/m 3 ) blows over the top. P 1 +!gy 1 +!!v 1 = P +!gy +!!v P 1 P =!! (v v 1 ) F = P A =!! (v v 1 ) =! (1.9) (30 ) N / m = 581 N/ m = 581 N/ m (15 m)(15 m) = 131,000 N = 9,000 pounds! Lecture 17 Purdue University, Physics 0 19 Define Strain = "L / L Stress = F/A Hooke s Law Revisited Hooke s Law Stress = Y*Strain F/A = Y *"L/L k = Y A/L from F = k "L Y (Young s Modules) independent of L or A Has the unit of pressure (i.e., pascal) Inherent stiffness of a material For many materials, Y is the same for compression and tension Lecture 18 Purdue University, Physics 0 0
Beyond Hook s Law What is harmonic motion? Ultimate Strength Elastic limit Proportional limit Breaking Point Examples: Lecture 18 Purdue University, Physics 0 1 Lecture 18 Purdue University, Physics 0