Question

An open feed water heater operates at steady state with liquid water entering inlet 1 at 10 bar, 50 degree C and a mass flow- rate of 60 kg/s. A separate stream of steam enters inlet 2 at 10 bar and 200 degree C. Saturated liquid at 10 bar exits the feed water heater at exit 3. Ignoring heat transfer with the surroundings and neglecting kinetic and potential energy effects, determine the mass flow rate, in kg/s, of the steam at inlet 2.

Answer 1

16.46 kg/s

Step-by-step explanation:

We solve this by writing an energy balance around the open feed water heater:

E,in=E,out

We know that heat transfer to surroundings and kinetic and potential energy are zero.

`m_1h_1+m_2h_2=m_3h_3`

We can use the thermodynamic tables for saturaed liquid and steam to solve for the enthalpies.

For inlet 1:

50°C, 10 bar

`h_1=209.31 kJ/kg`

For inlet 2:

steam, 10 bar, 200°C

`h_2=2778.1 kJ/kg`

For outlet 3:

Saturated liquid at 10 bar

`h_3=762.5 kJ/kg`

We can also perform a mass balance:

`m_1+m_2=m_3`

We can solve the energy balance:

`60\cdot{209.31}+m_2\cdot{2778.1}=(60+m_2)\cdot{762.5}`

`12558.6+2778.1\cdot{m_2}=762.5\cdot{m_2}+45750`

Solve for m₂

`m_2=33191.4/2015.6=16.47`