In this problem you will compare steady Bernoulli, Unsteady Bernoulli and a quasi-steady Navier-Stokes analysis to determine when the assumptions associated with each are valid. x = 0.5 sin(wt) [meters] 5m 1.0m Large volume Dia = 0.5cm Large volume Figure 1: A schematic of a piston damper system. Consider the oscillating piston damping system shown above. The fluid in the system is water at standard conditions Assume the temperature of the water does not change during the analysis. Ignore the losses associated with the flow entering the pipe. Answer the following & clearly state all assumptions. Draw and label all streamlines, control volumes and radial lines used. 1. Use the standard steady state Bernoulli Equation to determine the force required to move the piston back and forth for different pulsing frequencies (w). 2. Predict and plot the peak power required to move the piston as a function of w (Power F.V) 3. Use the unsteady Bernoulli Equation to determine the force required to move the piston back and forth for different pulsing frequencies (w). 4. Predict and plot the peak power required to move the piston as a function of w (Power F.V) 5. Use the steady state version of the Navier-Stokes equation to determine the force required to move the piston back and forth for different pulsing frequencies (w). 6. Predict and plot the peak instantaneous power required to move the piston as a function of w (Power = F.V) 7. Of these three analyses, which one is most accurate for different w values? 8. Discuss how you would get a more accurate prediction of the force and instantaneous power.