You have a large hydraulic cylinder with a piston diameter of 8.00 inches. The rod of the cylinder is extended 48 inches. The pressure inside the cylinder at time, t = 0.00 sec is 1,000 psig. There is a 10 foot long hose connected to the hydraulic cylinder. The diameter of the hose is 0.375 inches. The Bulk Modulus of system is 150,000 psi. At time, t = 0.00 sec the pressure at the end of the hose away from the hydraulic cylinder is increased to 2,000 psig. Dynamic viscosity is 4.061*10-5 lbf-sec/in2. The fluid has a specific weight of 50 lbf/ft3 under standard earth gravity.
Find: a) the time constant, tau, for the system at these conditions
b) How long will it take for the pressure to rise to 1,500 psig in the cylinder, assuming the piston does not move?