Question

Valve, R leves e9 Saint S EYE DIL Fig. 2. Hydraulic system Problem 3. A spring-loaded hydraulic accumulator is shown in Fig. 3. Hydraulic fluid flows into the accumulator with volumetric-flow rate Qin. The spring side of the accumulator has constant atmospheric pressure Parm. Derive an expression of the total capacitance C of the hydraulic accumulator. (Hint: the goal is to find an expression in the form CP = Qin. Hydraulic fluid volumetric-flow rate Area, A Hydraulic accumulator Fig. 3. Hydraulic accumulator.

Answer 1

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ده Capacitance det's the measure of change in press are due to the storage of Volume floul. c= Saudt - Sade on AP AP. Consider fluid entering a chamber, as in given figure, The fluid is compressible so that the amount of fluid within the chamber may be increased by compressing it and the volume of the chamber may be allowed to vary. Then from the continuity equabion ea = devre de de dt v=chamber volume e=fluid density 320 Q = a + ve de We assume small changes in pressure and therefore small changes in volume so that v = v tvt, P = 8 +pl, e=ētel where ylcal so vai e cal so e=é So, Queen andere

alus 907 df - de so Q = Bz Bulk Modulus dy + I do B dt | c= Sadt = due t o АР Now take Spring loaded piston. P Palio = PA PA Force balance kx 7 PatmA = PA dx= small displacement Koc = (P-Patma x = SPA SpA -Kx=0 Adp= kax - kdr 2 So C= A + Mechanical Capacitorose Compressibity Capacitance, Qon vtworf sip Din = Cip when compressibilty Corp a citance is neglected an - P = x 3 lý - CP v=volume of or ID