Water enters the 20 41cmdiameter superheater tubes shown her

Water enters the 20- 4.1-cm-diameter superheater tubes shown here as a saturated vapor at 6 MPa and leaves at 6 MPa, 450 oC with a velocity of 35 m/s. Calculate the water velocity (in m/s) and volumetric flow rate (in m3/s) at the inlet to the entire tube bundle.

Solution

Let state 1 indicates inlet to the superheater tubes and state 2 indicates the outlet of the superheater tubes.

Velocity of steam at outlet of tubes V₂ = 35 m/s.

No of tubes, n=20

Diameter of each tube, d = 4.1 cm = 0.041 m

Area of cross section of each tube, a= 22/7*d²/4

a = 22/7 * (0.041)²/4

= 0.00132 m²

Total area of cross section of all 20 tubes, A= n.a

A = 20X0.00132 = 0.0264 m²

From steam tables,

at 6 MPa, Specific Volume of saturated vapour, v₁= 0.03244 m³/kg.

at 6 MPa and 450^o C, Specific volume of superheated steam, v₂= 0.05214 m³/kg.

Now from the continuity equation at inlet 1 and outlet 2 of the tubes,

Mass flow rate at inlet 1 = mas flow rate at outlet 2

m = density₁.A₁.V₁ = density₂. A₂.V₂

where is the density of steam which is also equal to reciprocal of specific volume, v.

density = 1/v.

Substituting value of density = 1/v, and since A₁= A₂

V₁ / v₁ = V₂ / v2

Water Velocity at the inlet to entire tube bundile, V₁

V₁ = V₂. v1/v2

=  35 x (0.03244)/(0.05214) m/s

= 21.78 m/s

Volumetric flow rate of water at the inlet to the entire tube bundle, Q₁= A₁ x V₁

Q₁ = 0.0264 x 21.78

= 0.0575 m³/s.