Question

A Pump supplies oil at $0.002m^3/sec.$ to a 50 mm diameter double acting cylinder and a rod diameter is 20 mm. If the load is 6000 N bolts in extending and retracting stroke, the piston velocity during the extension and retraction stroke are

• A. $2m/sec,2.3m/sec$
• B. $1m/sec,1.2m/sec$
• C. $1.2m/sec,1.5m/sec$
• D. $1.5m/sec,1m/sec$

Answer 1

The correct option is B $1m/sec,1.2m/sec$

$\text{Oil flow rate from pump}\left(Q_{in}\right)=0.002m^3/sec\text{Diameter of the cylinder (D)}=50mm=0.05m\text{Diameter of the rod (d)}=20mm=0.02m\text{Load during extension and return stroke (F)}=6000N.\text{Piston velocity during extension stroke}\left(V_1\right)=\frac{Q_{in}}{Ap}=\frac{0.002}{\frac{\pi }{4}\left(D^2\right)}=\frac{0.002\times 4}{\pi (0.05{)}^2}=1m/sec.\text{Piston velocity during return stroke}\left(V_2\right)=\frac{Q_{in2}}{Ap-A_r}=\frac{0.02}{\frac{\pi }{4}(D^2-d^2)}=\frac{0.02}{\frac{\pi }{4}({0.05}^2-{0.02}^2)}=1.2m/sec.$