Figure 1 shows a desuperheater a steadyflow device in which

Figure 1 shows a desuperheater, a steady-flow device in which 100kg/s of superheated steam are combined with cooler liquid water to produce a stream of saturated steam Heat losses to the surroundings are Q=-2000kJ/s. Determine the required massflowrate m_2 of liquid water, in kg/s. State clearly all assumptions you make in your analysis. The superheated steam is delivered to the desuperheater in five large pipes, each 0.5m in diameter. If the mass flow mi is divided equally among the pipes, determine the velocity of the superheated steam (m/s) in a pipe.

Solution

Steam at 5 bar 200 C

h1 = 2860 kJ/kg

Liquid water at 5 bar 25 C

h2 = 105 kJ/kg

steam saturated at 5 bar

h3 = 2750 kJ/kg

applying consrvation of energy

Q    =   (m1 + m2) * h3 - m1 * h1 - m2 * h2

-2000 = (100 + m2) * 2750 - 100 * 2860 - m2 * 105

m2 = 3.402646 kg/s

b) mass flow rate in one pipe = 100 /5 = 20 kg/s

     density of steam = 2.35 kg/m^3

     velocity of flow   =   mass flow rate / (density * Area of pipe)

     V = 20 / (2.35 * pi * 0.5^2/4)   = 43.344 m/s