Question

A hot water heater tank is initially filled with 300 L of hot water at 52◦C. Hot water at 52◦C exits the tank through a 2cm diameter hose at 0.5 m/s velocity. If cold water at 12◦C enters the tank at rate of 5 L/min, determine the mass of water in tank after 10 minutes. Assume the pressure in tank remains constant at 1 atm.

Answer 1

Answer:

$m_2= 255.76Kg$

Explanation:

For the resolution of the problem we first determine the initial mass in the tank and the amount that is coming out of water, both cold and hot during the given time, with this we will have the final mass in the tank, as well.

Mass in the tank,

$m_i=\rho V\\m_i=1000*0.3\\m_i=300kg$

Hot water body in 10 minutes of departure,

$m_h=\rho  A_t V \Delta t\\m_h = 1000*\frac{\pi}{4}d^2(0.5)(10*60)\\m_h= 1000*\frac{\pi}{4}(0.02)^2(0.5)(10*60)\\m_h= 94.24Kg$

Cold water body in 10 minutes,

$m_c = \rho V_c \Delta t \\m_c = 1000*0.005*10\\m_c =50Kg$

So the final mass

$m_2 = m_i+m_c-m_h\\m_2 = 300+50-94.24\\m_2= 255.76Kg$