Answer to Question #172628 in Mechanical Engineering for April

Question

A 0.0856 m3 drums contains saturated water and saturated vapor at 370oC. (a) Find the mass of each if their volumes are equal. What is the quality? (b) Find the volume occupied by each if their masses are equal.

Answer 1

Density of water at 100°C (as water cannot be hotter than 100°C) is 958 kg/m³.

Pressure of saturated vapor at 370°C is

$$p_{ws}=\frac{\exp(77.3450 + 0.0057 T - 7235 / T)}{T^{8.2}}=18,575,161\text{ Pa}.$$

Density of vapor:

$$\rho_{ws}=\frac{0.0022p_{ws}}{T}=63.5\text{ kg/m}^3.$$

(a) The volume of water or steam is  0.0428 m³. The mass of each volume is

$$m_w=V\rho_w=0.0428·958=41.0\text{ kg},\\ m_{ws}=V\rho_{ws}=2.72\text{ kg}.$$

(b) To find volumes, use the equations above:

$$V_w=\frac{m}{\rho_w},\\\space\\ V_{ws}=\frac{m}{\rho_{ws}},\\\space\\ V=V_w+V_{ws}=m\bigg(\frac{1}{\rho_{ws}}+\frac{1}{\rho_w}\bigg),\\\space\\ m=V\frac{\rho_w\rho_{ws}}{\rho_w+\rho_{ws}}=5.10\text{ kg}.$$

The volumes:

$$V_w=\frac{5.10}{958}=5.32·10^{-3}\text{ m}^3,\\\space\\ V_{ws}=\frac{5.10}{63.5}=0.0803\text{ m}^3.$$