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PHYSICS 231 Lecture 22: fluids and viscous flow

PHYSICS 231 Lecture 22: fluids and viscous flow. Remco Zegers Walk-in hour: Tue 4-5 pm Helproom. P 0. h. B. w. Pressure at depth h. P = P 0 +  fluid gh h: distance between liquid surface and the point where you measure P. h. P. Buoyant force for submerged object.

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PHYSICS 231 Lecture 22: fluids and viscous flow

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  1. PHYSICS 231Lecture 22: fluids and viscous flow Remco Zegers Walk-in hour: Tue 4-5 pm Helproom PHY 231

  2. P0 h B w Pressure at depth h P= P0+ fluidgh h: distance between liquid surface and the point where you measure P h P Buoyant force for submerged object B = fluidVobjectg = Mfluidg = wfluid The buoyant force equals the weight of the amount of water that can be put in the volume taken by the object. If object is not moving: B=wobject object= fluid Buoyant force for floating object The buoyant force equals the weight of the amount of water that can be put in the part of the volume of the object that is under water. objectVobject= waterVdisplaced h= objectVobject/(waterA) PHY 231

  3. Bernoulli’s equation P1+½v12+gy1= P2+½v22+gy2 P+½v2+gy=constant The sum of the pressure (P), the kinetic energy per unit volume (½v2) and the potential energy per unit volume (gy) is constant at all points along a path of flow. Note that for an incompressible fluid: A1v1=A2v2 This is called the equation of continuity. PHY 231

  4. hole in a tank P0 Pdepth=h =Pdepth=0+ gh h y If h=1m & y=3m what is x? Assume that the holes are small and the water level doesn’t drop noticeably. x PHY 231

  5. Viscosity Viscosity: stickiness of a fluid One layer of fluid feels a large resistive force when sliding along another one or along a surface of for example a tube. PHY 231

  6. Viscosity Contact surface A moving F=Av/d =coefficient of viscosity unit: Ns/m2 or poise=0.1 Ns/m2 fixed PHY 231

  7. Poiseuille’s Law How fast does a fluid flow through a tube? R4(P1-P2) (unit: m3/s) Rate of flow Q= v/t= 8L PHY 231

  8. Example Flow rate Q=0.5 m3/s Tube length: 3 m =1500E-03 Ns/m2 PP=106 Pa P=105 Pa What should the radius of the tube be? PHY 231

  9. If time permits, I will do additional problems here. PHY 231

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