An emergency relief valve is installed on a reactor to relieve excess pressure in case of a runaway reaction. The lines upstream and downstream of the valve are 6 in. sch 40 pipe. The valve is designed to open when the tank pressure reaches $100 \mathrm{psig}$, and the vent exhausts to the atmosphere at $90^{\circ}$ to the direction entering the valve. The fluid can be assumed to be incompressible, with an $\mathrm{SG}$ of 0.95 , a viscosity of $3.5 \mathrm{cP}$, and a specific heat of $0.5 \mathrm{Btu} / \mathrm{lb}_{\mathrm{m}}{ }^{\circ} \mathrm{F}$. If the sum of the loss coefficients for the valve and the vent line is 6.5 , determine

(a) The mass flow rate of the fluid through the valve in $\mathrm{lb}_{\mathrm{m}} / \mathrm{s}$ and the value of the Reynolds number in the pipe when the valve opens.

(b) The rise in temperature of the fluid from the tank to the vent exit, if the heat transferred through the walls of the system is negligible.

(c) The force exerted on the valve supports by the fluid flowing through the system. If you could install only one support cable to balance this force, show where you would put it.