(See The Wide World of Fluids article titled "Smart Shocks," Section 5.3.3.) A 200-lb force applied to the end of the piston of the shock absorber shown in Fig. P5.104 causes the two ends of the shock absorber to move toward each other with a speed of \(5 \mathrm{ft} / \mathrm{s}\). Determine the head loss associated with the flow of the oil through the channel. Neglect gravity and any friction force between the piston and cylinder walls.

Figure P5.104

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Gas Oil- Piston Channel 1-in. diameter p=0 200 lb