H20 at 2 bars and 150C is flowing through a pipe at a mass flowrate of 2 kg/s as it is being heated by an electrical resistance in the pipe. At the exit of the pipe (whose diameter does not change), the temperature of H20 increases to 250C as its pressure stays constant at 2 bars. 1) Determine the size of the heater needed (in terms of the amount of heat transfer needed for steady state operation), 2) Determine the change in flow speed between the inlet and the outlet

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ajeigbeibraheem ajeigbeibraheem · Answer 1 · 2020-03-13T11:36:27+01:00

Answer:

1) 404.36 KW

2) 1.25 V₁

Explanation:

1) The size of the heater needed (in terms of the amount of heat transfer needed for steady state can be calculated by using the formula:

[tex]Q_{in} = m(h_2-h_1)[/tex]

For state 1;

H20 = 2 bars and 150° C; then from super-heated steam tables;

h₁ = 2768.78 kJ/kg ; s₁ =1.042 kg/m³

For state 2;

H20 = 2 bars and 250° C; then from super-heated steam tables;

h₂ = 2970.96 kJ/kg ; s₂ = 0.834 kg/m³

∴ [tex]Q_{in} = m(h_2-h_1)[/tex]

[tex]Q_{in}[/tex] = 2(2970.96 - 2768.78)

[tex]Q_{in}[/tex] = 404.36 KW

2) Determine the change in flow speed between the inlet and the outlet

Given that: A₁ = A₂

However, the mass flow rate remains constant;

then: m₁ = m₂

∴ [tex]s_1A/__1}}V_1[/tex] = [tex]s_2A/___2}}V_2[/tex]

1.042V₁ = 0.834V₂

V₂ = 1.25V₁

∴ The change on flow speed between the inlet and the outlet = 1.25V₁