Water flows through the tubes of a boiler. The water enters a tube of diameter 0.13m under
pressure 7 MPa and temperature 65°C and leaves the tube as superheated steam (6 MPa, 450°C). If
the outlet velocity of the steam is 80m/s, calculate the velocity and volume flow rate at the inlet.
To calculate the velocity and volume flow rate at the inlet, we can use the principle of conservation of mass and the properties of the fluid.
1. Calculate the density of water at the entrance:
a. Convert the pressure from MPa to Pa: 7 MPa = 7 x 10^6 Pa
b. Convert the temperature from Celsius to Kelvin: 65°C = 65 + 273.15 K
c. Use the steam tables or water properties tables to find the density of water at the given pressure and temperature.
2. Find the velocity at the inlet:
a. Apply the principle of conservation of mass, which states that the mass flow rate at any point is constant.
b. Since mass flow rate (m_dot) = density (ρ) x velocity (v) x cross-sectional area (A), we can rearrange the equation to solve for velocity (v).
v = m_dot / (ρ * A)
c. Plug in the values of density (ρ) from step 1 and the diameter (D) of the tube (0.13m) to calculate the cross-sectional area (A = π * (D/2)^2).
d. Calculate the velocity (v).
3. Find the volume flow rate at the inlet:
a. Volume flow rate (Q_dot) = density (ρ) x velocity (v) x cross-sectional area (A).
b. Plug in the values of density (ρ) from step 1, the velocity (v) from step 2, and the cross-sectional area (A = π * (D/2)^2) to calculate the volume flow rate (Q_dot).
By following these steps, you will be able to calculate the velocity and volume flow rate at the inlet of the boiler.