Steam enters a long, horizontal pipe with an inlet diameter of D1 = 16 cm at 2 MPa and 300°C with a velocity of 2.5 m/s. Farther downstream, the conditions are 1.8 MPa and 250°C, and the diameter is D2 = 14 cm. Determine

(a) the mass flow rate of the steam and

(b) the rate of heat transfer. For this pipe system, the kinetic energy of the steam is negligible.

m = 0.4005 kg/s

Q_out = 45.1 KJ/s

Explanation:

Given

Pipe inlet diameter D1 = 16 cm

Steam inlet pressure P1 = 2 Mpa

Steam inlet temperature T1 = 300 °C

Pipe outlet diameter D2 = 14 cm

Steam inlet velocity V1 = 2.5 m/s

Steam outlet pressure P2 = 1.8 MPa

Steam outlet temperature T2 = 250 °C

Required

Determine

(a) The mass flow rate of steam.

(b) The rate of heat transfer.

Assumptions

Kinetic and potential energy changes are negligible.

This is a steady flow process.

There is no work interaction.

Solution

Part a From steam table (A-6) at P1 = 2 Mpa, T1 = 300 °C

vl = 0.12551 m^3/Kg

h1 = 3024.2 KJ/Kg

The mass flow rate of steam could be defined as the following

m = 1/v1*A1*V1

m = 0.4005 kg/s

Part b We take the pipe as our system. The energy balance could be defined as the following

E_in - E_out = ΔE_sys = 0

E_in = E_out

mh_1 = Q_out + mh_2

Q_out = m (h_1-h_2)

From steam table (A-6) at P2 = 1.8 Mpa T2 = 250 °C h2 = 2911.7 KJ/Kg The heat transfer could be defined as the following

Q_out = m (h_1-h_2)

Q_out = 0.4005 * (3024.2 - 2911.7) = 45.1 KJ/s