Properties of steam: 18 flashcards

The dryness fraction, denoted $x$, is the ratio of the mass of dry steam to the total mass of the mixture (dry steam + water droplets). It ranges from 0 (saturated water) to 1 (dry saturated steam).

For wet steam with dryness fraction $x$, the specific enthalpy is $h = h_f + x \cdot h_{fg}$, where $h_f$ is the specific enthalpy of saturated liquid and $h_{fg}$ is the latent heat of vaporization.

The specific volume of wet steam is $v = v_f + x \cdot v_{fg}$, where $v_f$ is the specific volume of saturated liquid and $v_{fg} = v_g - v_f$ (with $v_g$ being the specific volume of dry saturated steam). Often $v_f$ is negligible compared to $v_g$.

For dry saturated steam ($x=1$), the specific enthalpy is $h_g = h_f + h_{fg}$. This is the total heat content per unit mass at the saturation temperature corresponding to the given pressure.

Superheated steam is steam heated above its saturation temperature at a given pressure. Its enthalpy is $h = h_g + c_p (T_{sup} - T_{sat})$, where $c_p$ is the specific heat at constant pressure, $T_{sup}$ is the superheated temperature, and $T_{sat}$ is the saturation temperature.

Using $h = h_f + x \cdot h_{fg}$: $h = 762.8 + 0.9 \times 2015.3 = 762.8 + 1813.77 = 2576.57$ kJ/kg.

First, $v_{fg} = v_g - v_f = 0.3749 - 0.001093 = 0.373807$ m³/kg. Then $v = v_f + x \cdot v_{fg} = 0.001093 + 0.85 \times 0.373807 = 0.001093 + 0.317736 = 0.318829$ m³/kg.

The degree of superheat is the difference between the actual temperature of superheated steam and its saturation temperature at the same pressure: $\Delta T_{sup} = T_{sup} - T_{sat}$.

As dryness fraction increases (more dry steam), the enthalpy increases because more latent heat is added. At $x=0$ (saturated water), enthalpy is $h_f$; at $x=1$ (dry saturated), it is $h_g$. For wet steam, it lies between these values.

Specific volume determines the size of pipes, ducts, and equipment needed to handle a given mass flow of steam. It also affects velocity and pressure drop calculations in steam distribution systems.

$h = 908.6 + 0.95 \times 1890.7 = 908.6 + 1796.165 = 2704.765$ kJ/kg.

Superheated steam has a higher specific volume than saturated steam at the same pressure because it is at a higher temperature, causing it to expand. The specific volume increases with the degree of superheat.

Locate the superheated steam table for the given pressure. Find the row corresponding to the superheated temperature and read the specific enthalpy directly. Alternatively, use $h = h_g + c_p (T_{sup} - T_{sat})$ if $c_p$ is known.

Using $v = v_f + x(v_g - v_f)$: $0.2 = 0.001 + x(0.4 - 0.001) = 0.001 + 0.399x$. So $0.199 = 0.399x$, giving $x = 0.4987$ (approximately 0.5).

The latent heat of vaporization ($h_{fg}$) is the amount of heat required to convert 1 kg of saturated liquid into dry saturated steam at constant pressure and temperature. It decreases as pressure increases.

Degree of superheat = $250 - 198.3 = 51.7$°C.

It is the specific enthalpy of liquid water at its saturation temperature, denoted $h_f$. It represents the sensible heat content of the liquid, and is obtained from steam tables at the given pressure.

Dryness fraction indicates the amount of moisture in steam. High moisture content can cause erosion of turbine blades, reduce efficiency, and affect heat transfer. Therefore, knowing $x$ helps in controlling steam quality for safe and efficient operation.