Question

The specific volume of steam after expansion

in turbine is 13 m3/kg. At this pressure the

saturated liquid and saturated vapour specific

volume are 0.002 m3/kg and 16 m3/kg

respectively. Find the dryness fraction of the

steam.​

Answer 1

Explanation:

The specific volume of steam after expansion in the turbine is 13 m3/kg. The specific volumes of saturated liquid and saturated vapor at this pressure are 0.002 m3/kg and 16 m3/kg respectively. The value of dryness of steam is

Answer 2

Answer:

The dryness fraction of the steam measured is 20.65

Explanation:

Given,

The specific volume of steam after expansion, V = 13 m³/Kg

The specific volume of saturated liquid, $V_{l}$ = 0.002 m³/Kg

The specific volume of saturated vapour, $V_{v}$ = 16 m³/Kg

The steam's dryness fraction, X =?

As we know,

• The dryness fraction of steam helps in determining the amount of water within the steam.

The dryness fraction of steam can be calculated by using the equation of specific volume of steam given below:

• $V = X \times V_{v} \times (1 -X) \times V_{l}$

After putting all the given values in the equation, we get:

• $13 = X \times 16 \times (1 -X) \times 0.002$
• $13 = 0.032X \times (1 -X)$
• $13 = 0.032X - 0.032X^{2}$
• $0.032X^{2} - 0.032X + 13 = 0$

After solving the equation for X by quadratic formula,

• $\frac{-b - \sqrt{b^{2} - 4ac } }{2a}$

Here, a = coefficient of $X^{2}$ , b = coefficient of X , c = constant

We get two values of X

• X = -19.5 or 20.65

As dryness fraction cannot be negative, so the value of X = 20.65.

Hence, the dryness fraction of the steam, X = 20.65.