Question Solved1 Answer Fluid Mechanics HD- Circular Puck V A circular disk-shaped puck for an air hockey table has mass m and diameter D. When hit, the puck has an initial velocity of V. The puck is cushioned by a thin air film of height h and viscosity p as it travels across the table. Derive an expression for the velocity of the puck as a function of time. You may assume that velocity profile of the air within the gap instantly adjusts itself to the instantaneous conditions of the puck. Justify your answers and show all of your work to receive full credit. h M Air Hockey Table

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Fluid Mechanics
Transcribed Image Text: HD- Circular Puck V A circular disk-shaped puck for an air hockey table has mass m and diameter D. When hit, the puck has an initial velocity of V. The puck is cushioned by a thin air film of height h and viscosity p as it travels across the table. Derive an expression for the velocity of the puck as a function of time. You may assume that velocity profile of the air within the gap instantly adjusts itself to the instantaneous conditions of the puck. Justify your answers and show all of your work to receive full credit. h M Air Hockey Table
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Transcribed Image Text: HD- Circular Puck V A circular disk-shaped puck for an air hockey table has mass m and diameter D. When hit, the puck has an initial velocity of V. The puck is cushioned by a thin air film of height h and viscosity p as it travels across the table. Derive an expression for the velocity of the puck as a function of time. You may assume that velocity profile of the air within the gap instantly adjusts itself to the instantaneous conditions of the puck. Justify your answers and show all of your work to receive full credit. h M Air Hockey Table
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The detailed explanation of the derivation with assumptions is given below:-Q.Given data: -Initial velocity of puck is V_(0)puck is cuthioned by a thin air film of height h and viscosity mu as it travelsNow, Assumptions: -i) No other effects acting on the circular puck except the vicous force.ii) Velocity profile of air within the thin gop instantly adjusts itself to the instantaneous conditions of the peck.iii) Air followes Newton's law of viscosity. Let the velocity of the puck at some instant t is Vm//s.Now, By Newton's law of Escosity. Shear stress is directly broportional to the velocity gradient.{:[=>quad tau prop(dV)/(dh).],[=>quad tau=mu(dV)/(dh)quad{[" also assumed that "],[" The air film vis - "],[" cosity does not changu) "],[" with time "]:}],[=>quad tau=mu(V)/(h)quad{" By assumption (ui) "}". "]:}:. shear force due to viscosity isF_(mu)=mu(V)/(h)*A{ Where A is the area of puck in the contact with the air folm.:.A=(pi)/(4)D^(2)so, F_(mu)=mu(V)/(h)((pi)/(4)D^(2))=(1).Since, this force is acting is in the opposite direction of motion, :. it will froduce deacceleration in the motion of puck.Now ... See the full answer