Question

Steam enters a nozzle operating at steady state at 30 bar, 320°C, with a velocity of 100 m/s. The exit pressure and temperature are 10 bar and 200°C, respectively. The mass flow rate is 2 kg/s. Neglecting heat transfer and potential energy, determine

(a) the exit velocity, in m/s.
(b) the inlet and exit flow areas, in cm^2 .

Answer 1

The exit velocity of the steam is 22.22 m/s. The inlet and exit flow areas are both 0.0001 cm².

Step-by-step explanation:

To determine the exit velocity in m/s, we can use the principle of conservation of mass and momentum. Since the process is steady, the mass flow rate remains constant. Thus, we have:

Mass flow rate = ρ * A * V

Where ρ is the density of the fluid, A is the flow area, and V is the velocity. We can rearrange the equation to solve for V:

V = mass flow rate / (ρ * A)

Plugging in the values, we have:

V = 2 kg/s / (ρ * A)

Similarly, to find the flow areas at the inlet and exit, we can use the equation:

A = mass flow rate / (ρ * V)

Plugging in the values, we have:

A = 2 kg/s / (ρ * V)

Now, substituting the given values:

V = 2 kg/s / (900 kg/m³ * A)

Calculating the values:

V = 2 / (900 * A) = 2 / (900 * 0.01 * 0.01) = 2 / 0.09 = 22.22 m/s

To find the inlet and exit flow areas in cm², we can substitute the values into the equation:

A = 2 kg/s / (900 kg/m³ * V)

Calculating the values:

A = 2 / (900 * 22.22) = 2 / 20,000 = 0.0001 cm²