Question 14.5: An intensifier supplies water at a pressure of 24 MPa to a h......
An intensifier supplies water at a pressure of 24 MPa to a hydraulic pressure machine. The diameter of the ram and the sliding cylinder of the intensifier are 0.15 m and 0.8 m respectively. Find the pressure of low pressure water entering the intensifier. The loss due to package friction can be taken as 5% of the total load on each packing.
Given: p_2=24 MPa =24 \times 10^6 N / m ^2 ; D_2=0.15 m ; D_1=0.8 m ; F=5 \% \text { in each packing. }
Upward force exerted by high pressure liquid on the sliding cylinder
=p_2 A_1\left(1-\frac{F_r}{100}\right)=24 \times 10^6 \times \frac{\pi}{4}0.15^2(1-0.05)=402909 N
Downward force exerted by low pressure liquid on the sliding cylinder
=p_1 A_1\left(1-\frac{F_r}{100}\right)=p_1 \times \frac{\pi}{4}0.8^2 \times(1-0.05)=0.4775 p_1 N
Equating the two forces, we get
40299=0.4775 p_1
Pressure of entering water, p_1=\frac{402909}{0.4995}=843749 Pa =843.75 kPa