Calculate work should be done (in$$ $$J) in order to squeeze all water from a horizontally located cylinder as shown in figure during the time t $$=$$ $$10$$ s by means of a constant force acting on the piston? The volume of water in the cylinder is equal to V $$=$$ $$1$$ lit, the $$cross-sectional$$ area of the orifice is a $$=$$ $$0.5$$ $$cm2$$, with a being considerably less than the piston area. The friction and viscosity are negligibly small.

Question

Infinity Learn · Accepted Answer

Work done to squeeze $$water=F$$⋅LIf v be the velocity at point B, then applying Bernoull theorem at points ‘$$1$$’ and ‘$$2$$’, we have      $$P1+12$$ρ$$v12=P2+12$$ρ$$v22Here$$ $$P1=P0+FA$$ and $$P2=P0also$$ $$v1$$ is very much smaller than $$v2$$, can be neglected here we $$haveP0+FA=P0+12$$ρ$$v2$$         …(i)Force$$ on piston $$F=P$$⋅$$A=12$$ρ$$v2A$$         …$$(ii)Volume$$ of liquid coming through orifice per unit time $$=$$ a vVolume of liquid coming through during time 't' V $$=$$ a v tVelocity of liquid through orifice $$v=VatFrom$$ Eqs. $$(i) and (ii) $$F=12$$ρ$$Vat2AThus$$ work done is $$W=FL=12$$ρ$$VatAL=12$$ρ$$Vat2Vhence$$ $$W=12$$ρ$$V3a2t2=1210001000$$×$$10$$−$$630.5$$×$$10$$−$$42102=2.0J$$

Best Courses for You

Detailed Solution

courses

Get Expert Academic Guidance – Connect with a Counselor Today!