During a test of a hydraulic brake system, a minor leak in one of the lines allows 10 % of the fluid volume displaced by the master cylinder to escape each time the brakes are applied. The system parameters are: master-cylinder piston area 2.8 cm2, two front wheel pistons each of area 6.0 cm2, and two rear wheel pistons each of area 4.0 cm2. The driver applies a steady force of 500 N on the master-cylinder piston.
(i) If no leak were present, calculate the force transmitted to one front-wheel piston.
(ii) Show that, under the stated conditions, a loss of 10 % of the displaced fluid volume before it reaches the wheel cylinders results in a 10 % reduction in the pressure delivered to those cylinders.
(iii) Using the conclusion in part (ii), compute the actual force that now reaches one front-wheel piston.
(iv) Determine the additional force the driver would have to apply at the master cylinder to restore the original (leak-free) force on a front-wheel piston, assuming the percentage loss of displaced volume remains the same.