Question

A water heater shower needs to supply warm water at temperature of 40°C. The hot water input is at 90°C and flowing with a flow rate of 0.5 kg/s at one side. On the other side, a stream of cold water flowing at 25°C. If we need the shower to supply water at 40°C at the exit, calculate the mass flow rate that is suitable for the cold water side. Assume all stream at equal pressure of 250 kPa.

Answer 1

The mass flow rate is the mass of a liquid substance passing per unit of time. In other words, the mass flow rate is defined as the rate of movement of liquid passing through a unit area. The mass flow is directly dependent on the density, velocity of the liquid, and area of cross-section. It is the movement of mass per unit time. The mass flow is denoted by m and the units in kg/s.

$m=ρVA$

$Q = mC(T_1-T_2)$

$m =\frac{0.5}{0.385\times(90-40)}= \frac{0.5}{25.025}=0.025 kg$

mass flow rate that is suitable for the cold waterside

$Q_c = mC(T_1-T_2) =0.025\times 0.385\times (90-25)= 0.62 \frac{kg}{s}$