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Energy Analysis of Control Volumes at Steady StateAir
Chapter 4, Problem 26P(choose chapter or problem)
Air enters a horizontal, constant-diameter heating duct operating at steady state at \(290 \mathrm{~K}, 1 \mathrm{bar}\), with a volumetric flow rate of \(0.25 \mathrm{~m}^3 / \mathrm{s}\), and exits at \(325 \mathrm{~K}\), 0.95 bar. The flow area is \(0.04 \mathrm{~m}^2\). Assuming the ideal gas model with = 1.4 for the air, determine (a) the mass flow rate, in \(\mathrm{kg} / \mathrm{s}\), (b) the velocity at the inlet and exit, each in \(\mathrm{m} / \mathrm{s}\), and (c) the rate of heat transfer, in kW.
Questions & Answers
QUESTION:
Air enters a horizontal, constant-diameter heating duct operating at steady state at \(290 \mathrm{~K}, 1 \mathrm{bar}\), with a volumetric flow rate of \(0.25 \mathrm{~m}^3 / \mathrm{s}\), and exits at \(325 \mathrm{~K}\), 0.95 bar. The flow area is \(0.04 \mathrm{~m}^2\). Assuming the ideal gas model with = 1.4 for the air, determine (a) the mass flow rate, in \(\mathrm{kg} / \mathrm{s}\), (b) the velocity at the inlet and exit, each in \(\mathrm{m} / \mathrm{s}\), and (c) the rate of heat transfer, in kW.
ANSWER:Step 1 of 2
Part b
We are required to calculate the mass flow rate.
Given data:
K
atm
N/m2
Therefore, the specific volume,
K
bar
N/m2
Therefore, the specific volume,
From the relation,
From the energy rate balance equation,
…..(1)
From table A-22, at K and
atm
kJ/kg
At
K and
bar
kJ/kg
Substitute these values and in equation (1),
m/s
So, m/s
The required velocities are 410 m/s and 488.6 m/s.