Chapter 10, Problem 12P

To determine

The largest size vehicle is to be found which can be lifted by hydraulic lift having maximum gauge pressure of $17atm$ .

Answer to Problem 12P

The largest size of vehicle which can be lifted is $10824.63kg$

Explanation of Solution

Given info:

Maximum gauge pressure, $P=17atm=17\times 1.013\times {10}^{5}Pa=1.7221\times {10}^{6}Pa$

Diameter of output line, $d=28cm=0.28m$

Formula used:

Radius, $r=\frac{d}{2}$

Area of output line, $A=\pi r^2$

Force, $F=PA=mg$

Calculation:

Substituting values in formula of radius,

  $r=\frac{0.28}{2}=0.14m$

Substituting values in formula of area,

  $A=\pi {(0.14)}^2=0.0616m^2$

Substituting values in formula of force,

  $\begin{array}{l}m(9.8)=(1.7221\times {10}^6)(0.0616)\\ m=\frac{(1.7221\times {10}^6)(0.0616)}{9.8}\\ m=10824.63kg\end{array}$

Conclusion:

The largest size of vehicle which can be lifted is $10824.63kg$