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2.007 –Design and Manufacturing I Pneumatics: and fluid flow more generally

2.007 –Design and Manufacturing I Pneumatics: and fluid flow more generally. Dan Frey. What are the Losses in the Tube When You Fill the Balloon?. ¼ inch ID tube 7 feet long 35 liters per minute flow rate. What are the Losses in the Tube When You Fill the Balloon?.

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2.007 –Design and Manufacturing I Pneumatics: and fluid flow more generally

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  1. 2.007 –Design and Manufacturing IPneumatics: and fluid flow more generally Dan Frey

  2. What are the Losses in the Tube When You Fill the Balloon? • ¼ inch ID tube • 7 feet long • 35 liters per minute flow rate

  3. What are the Losses in the Tube When You Fill the Balloon? • 35 liters per minute flow rate • ¼ inch ID tube • 7 feet long • About 0.3 psi

  4. Flow in a Pipe • This is called a “Moody diagram”

  5. What Losses are Worse, the Ones in the Table or the Ones in your Robot? • 35 liters per minute flow rate • 1/8 inch ID tube • 7 inches long • About 0.7 psi

  6. Flow in a Pipe • This is called a “Moody diagram”

  7. Euler and Streamline Curvature • Pressure gradient perpendicular to streamline

  8. Euler and Streamline Curvature • So, just about 4 in height diff between the edge and the center

  9. What Does this Tell You About Centrifugal Pumps and Balloons? • A BP-05 at 262 rpm with 5 cm radius spinning water can produce a pressure rise of 4 in of water • You need about 1 psi (~30 inches water, almost 10X) • You are spinning air, not water (about 1000X) • So pressure/density is a 10,000X deficit • Pressure/density rise goes like w2R2 (tip velocity squared) • To get a 10,000X increase, you need 100X in wR (tip velocity) • If you stay at 5cm radius, you need a motor that runs at 26,000 rpm at your chosen voltage (also 1psi*35*liter/min=4Watts) • Or, with a slower motor (e.g., BP-05, take off the 40:1 gear box and increase the radius or voltage by a factor of 5) Also consider efficiency BUT, the effect in the water experiment is only about HALF the story

  10. Bernoulli’s Equation • Inertia forces >> viscous forces • Applies along a streamline • Constant density • Steady flow (this form of the eqn) http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/lecture-28/

  11. Bernoulli’s Equation Static pressure Dynamic pressure (kinetic energy per unit volume) Gravitational potential energy per unit volume http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/lecture-28/

  12. Classic Application of Bernoulli:Water Flow from a Pressurized Tank • Fill the 2 liter bottle partially with water • Let’s pump the bottle to 30psi gauge • When I release the clamp, how high will the water go?

  13. Here is my approach • Go check out “water height problem v5.mcd” on Stellar

  14. Implication of Bernoulli:The Venturi Effect • Reducing cross sectional area causes • Velocity to rise (inversely proportional to area) • Dynamic pressure (rises as velocity squared) • So, static pressure drops • Can be used to measure flow velocity Pitot tube

  15. How an Air Speed Indicator Works • Total pressure indicated by ram air • Static pressure collected also • Difference measured and amplified by diaphragm • Mechanism converts into dial indication

  16. Other Implication of Bernoulli:Diffusers in Compressors • In the spinning water problem, pressure rise was • But we also imparted velocity to the flow, and we could recover some static pressure rise from that Dixon, Fluid mechanics and thermodynamics of turbomachinery http://library.books24x7.com.libproxy.mit.edu/book/id_36368/

  17. Viscous Forces in Flows • There is some velocity distribution • At the surface, the shear stress is y V(y) v(y)=m(dV/dy)

  18. Plane Poiseuille Flow • If viscous forces >> inertia forces • Velocity distribution is parabolic V(y) y h x

  19. Poiseuille and Connecting • Prof. Gossard’s connector • A very simple thing I can analyze • Assume 0.001inch slip fit all along intersection

  20. Plane Poiseuille Flow • h=0.001 inch • dp=1psi • dx=7mm • m=3.5x10-7lb*sec/ft^2 • W=p*0.315inch • Q=0.12 liter/min y V(y) x So, quite a slow leak.

  21. Plane Poiseuille Flow:Check the Assumptions • Q=0.12 liter/min • h=0.001 inch • W=p*0.315inch • V= Q/(h*W) = 3m/s • Re=6.0 y V(y) x So, dominated by viscous forces.

  22. Plane Poiseuille Flow:Check the Forces Involved y • Force ≈ 1/20 lb x So, no trouble keeping it on.

  23. Pneumatic System The whole thing is ~ 0.2 kg Cylinder 50 gr Valve 25 gr Bottle, fitting, hose, etc, 50 gr What can I do with it? How much: force? energy? power?

  24. How much work does it take to fill a 2 liter bottle to 60 psi? 15psi 15psi First, how much air do we need? We assume constant temperature, so PV=const. Note: Atmospheric pressure is about 15psi (14.7psi) NOTE: We are talking about 60psi on the gauge, that’s about 75 psi absolute. So P1V1=P2V2 and since the ratio of pressures is 5:1, so is the ratio of volumes. It takes ~10 liters of air from atmospheric conditions. 15 psi 75psi 15psi 15psi

  25. F1 How much work does it take to fill a 2 liter bottle to 60 psi? 15psi A quick estimate. F2~4000N A=(10cm)^2 15psi The relationship is not linear really, we’ll think about that next. F2 15 psi 75psi 20cm 15psi x 20cm 100cm Assuming a linear change in force W=area under the curve = ½ * 4100N*80cm~1600J This is an OVER estimate 15psi

  26. F1 How much work does it take to fill a 2 liter bottle to 60 psi? 15psi P2=75psi A refined estimate. A=(10cm)^2 15psi F2 What is this, physically? 15 psi 75psi 10 liters. 15psi V 2 liters P1=15psi 10 liters 15psi

  27. Comparison • Assuming 60 psi • 5 lbf • 2 inch stroke • <0.1 sec • >11W • SY113-SMO Solenoid Actuated Valve • Maximum flow rate = 10 liters / minute • Displacement of cylinder 4cm^3 Pneumatic actuators in the kit > 2X more powerful even though they are lighter.

  28. Comparison • Assuming 60 psi • 5 lbf • 2 inch stroke • 0.1 sec • ~11W • Assuming 3V • 0.5 Nm • 30 rpm • 1.5W • 4W at 4.8V Pneumatic actuators in the kit roughly 2X more powerful even though they are lighter.

  29. Compressed Air: Benefits • Simple linear motion • High forces • Rapid motion • Potential for high power in a small, light package

  30. Compressed Air: Hazards • High forces • Rapid motion • Potential for high power Show movie

  31. Next Steps • Spring break next week • Lab open from 8:30AM to 4:30 PM Monday to Thursday • Lab closed Friday • HW#4 will be issued Tuesday after break • It will be short, like 2 hours • Due 1.5 weeks later on 7 April • Exam #2 will be Thursday 14 April

  32. Adiabatic and Isothermal Processes

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