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4. A spring-loaded hydraulic accumulator is shown in the figure below. Hydraulic fluid flows into the accumulator with volumetric-flow rate Qin. The "spring side" of the accumulator has constant atmospheric pressure Patm. Derive an expression for the total capacitance of the hydraulic accumulator. Neglect the mass and friction of the accumulator piston. [Hint: the goal is to find an expression in the form C Pldt = Qin. Begin with the basic pressure- rate equation for the Control Volume and replace dVidt by an equation in terms of Pidt by noting that a differential change in pressure is balanced by a differential displacement of the piston or plate with area A.) Hydraulic fluid volumetric-flow rate P ww lin Р. am Area, A Hydraulic accumulator