lecture8-fluid%20dynamics%20applications0 - So far …...

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Unformatted text preview: So far … •  •  •  •  •  Density, ρ = m/V pressure, p = F/A, and Pascal’s principle buoyancy equa?on of con?nuity Bernoulli’s equa?on •  applica?ons today PHYSICS 101 help sessions & office hours for Dr. Heiner Monday Tuesday Wednesday 10 – 11 AM Thursday Friday office hours HENN 405 11AM – 12PM TA help sesssion HEBB 13 12 – 1 PM TA help sesssion HEBB 13 1 – 2 PM 2 – 3 PM PHYS 101 sec?on 102 3 – 4 PM office hours HENN 405 4 – 5 PM TA help sesssion HEBB 13 PHYS 101 sec?on 102 TA help sesssion HEBB 13 TA help sesssion HEBB 13 PHYS 101 sec?on 102 TA help sesssion HEBB 13 Two Questions Assume that water flows through a round pipe with a certain flow rate Δm/Δt (or ρ ΔV/Δt). At some point the diameter of the pipe decreases to half of its former value. Q1) The acceleration of the fluid in the narrow section A.  increases. A1 A2 B.  decreases. C.  remains the same. Q2) The force of the fluid in the narrow section A.  increases. B.  decreases. C.  remains the same. 3 Question The unknown (?) volume flow rate through the pipe is: A.  0.5 cm3/s B.  1.0 cm3/s C.  5.0 cm3/s D.  -1.0 cm3/s E.  -2.0 cm3/s changing flow dynamics in a pipe different diameter A1 v1 = A2 v2 equation of continuity For constant density Δh different heights 2 P + 1 2 ! v + ! gh = const Bernoulli’s equation breakdown Bernoulli’s 2 P + 1 2 ! v + ! gh = const Bernoulli’s equation if add a stopper, how would that affect the equation? Δh 0 2 P + 1 2 ! v + ! gh = const  P + ! gh = const What about a flowing fluid in a straight pipe (i.e., no Δh) ? Worksheet Typical blood pressure in an aorta is 13,600 Pa and its speed is 0.12 m/s. Blood passes through an area of aorta that has been narrowed down by plaque to a cross-sectional area 1/5 of normal aorta. (a)  What is the blood pressure as the blood passes the narrow part? (b)  What is the percentage change in the pressure? blocked Ques?on A blood platelet driTs along with the flow of blood through an artery that is par?ally blocked by deposits. As the platelet moves from the wide region to the narrow region, it experiences A.  an increase in pressure blocked B.  no change in pressure C. a decrease in pressure Special Case – Venturi Effect y1 = y2 Horizontal Pipe 12 12 P + ρ v1 = P2 + ρ v 2 1 2 2 12 P + ρ v = constant 2 •  In the region where the fluid speed increases the pressure in the fluid decreases. •  In the region where the fluid speed decreases the pressure in the fluid increases. Venturi Meter •  Measures pressure by reading the height of a fluid column. v1 A1 •  velocity  pressure  A2 v2 v  p  v1 A1 v  p  •  Height of the column in the small vertical tubes determined by the difference in pressure due to flowing fluid on the bottom and atmospheric pressure on top: measures gauge pressure. 10 Prairie Dogs V1 Burrows V2 Question Consider a straw in a glass of water. What happens to the water level in the straw if you blow horizontally across the top of the straw? 1) The water level drops. 2) The water level rises. 3) The water level stays the same. Bernoulli s Principle •  The velocity of a fluid is high in regions of low pressure, and small in regions of high pressure. •  Applications of Bernoulli s principle: shape of airplane wings, curved profile of sails, frisbee, jumping coins, jumping eggs, etc. 14 Ping Pong Ball Why does the ping pong ball try to return to the center of the jet? What forces are acting on the ball when it is not centered on the jet? Worksheet The drinking fountain outside your classroom shoots water about 16 cm straight up in the air from a nozzle of diameter 0.60 cm. The pump at the base of the unit (1.0 m below the nozzle) pushes water into a 1.8-cm-diameter supply pipe that goes up to the nozzle. 1. air 0.16 m 2. pipe 1.0 m Using the equation of continuity and Bernoulli’s equation, we will fill in the table below. pump 0.0 m 3. ...
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