BIEN 301 Lopez P 7.59 Rosalyn Pillow February 1, 2007.

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Presentation transcript:

BIEN 301 Lopez P 7.59 Rosalyn Pillow February 1, 2007

Joe can pedal his bike at 10 m/s on a straight level road with no wind. The rolling resistance of his bike is 0.80 N-s/m. The drag area (C D A) of Joe and his bike is m 2. Joe’s mass is 80 kg and that of the bike is 15 kg. He now encounters a head wind of 5.0 m/s.

(A) Develop an equation for the speed at which Joe can pedal into the wind. [Hint: A cubic equation for V will result.] (B) Solve for V, that is how fast can Joe ride into the headwind (C) Why is the result not 10 – 5 = 5 m/s as one might first suspect

Cr = 0.8 N-s/m V w = 5 m/s V j = 10 m/s C D A = m 2 m j = 80 kg m b = 15 kg C D = drag/(½ρV 2 A)

Perfectly symmetrical – pedal asymmetry negligible → C D = drag/½V 2 A, no moment Road remains smooth and level Joe exerts same power in both scenarios, thereby mathematically relating them Other drag variables are negligible – lift, pressure differences, etc

Drag = ½C D AρV 2 (Equation 1) Resistance = Cr(V)(Equation 2) ΣF = Drag + Resistance(Equation 3) P o = P 2 (Equation 4) P= FV(Equation 5) V= V j + V w every time in calculating the drag

F r1 = R*V o = 0.8 N-s/m*10 m/s = 8 N F joe,bike1 = ½ρ C D A V 2 = ½(0.422 m 2 )(1.2 m 3 )(10 m/s) 2 = N F o = F r + F joe,bike1 = N P o = F o V o = (33.32 N)(10 m/s) = J/s

Calculations Continued F 1 = ½C d Aρ(V j + V w ) 2 + C r (V j +V w ) F 1 = ½(0.422 m 2 )(1.2 kg/m 3 )(V j + 5) 2 + (0.8N-s/m)(V j + 5) F 1 = [0.2532(V j V j + 25) + 0.8V j + 4] N P 1 = F 1 V 1 = V j V j V j

Calculations part 3 P o = P = F 1 V = V j [0.2532(V j V j + 25) + 0.8V j + 4] 0 = V j V j V j V j = m/s

Why NOT? NOT 10 – 5 = 5 m/s = V both velocities cause air to flow over the drag area in the same direction, added then squared in the drag equation, and the wheel resistance which is linear must also be measured and included

This type of fluid mechanics involving drag, density, area and resistance on a macro level, can be applied to Estimate the time required for a medicine/radioactive isotope/nanoparticle to travel a specified distance through the body in and against various fluids.