The volumetric flow rate of air through a duct transition of the type shown in Table 12-9b (rectangular with two parallel sides) is 2 m3/s. The duct before the transition issquare, with a height of 50 cm. The expansion ratio across the transition is 4 (i.e., theduct area after the transition is 4 times greater than the duct area before the transition).a) Determine the pressure loss (in Pa) across the transition if the exit from the duct isabrupt (i.e., the diverging angle of the transition is 180º).b) Determine the percentage reduction in pressure loss for a transition diverging angleof 20º compared to the one in part (a).c) The head HVAC engineer requires the pressure loss across the transition to bereduced to less than 50% of the pressure loss for an abrupt exit (i.e., the case in part(a)), and suggests a transition diverging angle of 45º. Will this new diverging angleachieve the required reduction in pressure loss? Justify your answer.d) For a transition diverging angle of 90º, the pressure loss is found by a designer tobe higher than for an abrupt exit. Verify this result quantitatively, and explain whyreducing the angle of divergence increases the pressure loss relative to that for anabrupt exit for this case.table 12-9b from the heating, ventilating, and air conditioning textbook, sixth edition by faye c. mcquiston
The volumetric flow rate of air through a duct transition of the type shown in Table 12-
9b (rectangular with two parallel sides) is 2 m3
/s. The duct before the transition is
square, with a height of 50 cm. The expansion ratio across the transition is 4 (i.e., the
duct area after the transition is 4 times greater than the duct area before the transition).
a) Determine the pressure loss (in Pa) across the transition if the exit from the duct is
abrupt (i.e., the diverging angle of the transition is 180º).
b) Determine the percentage reduction in pressure loss for a transition diverging angle
of 20º compared to the one in part (a).
c) The head HVAC engineer requires the pressure loss across the transition to be
reduced to less than 50% of the pressure loss for an abrupt exit (i.e., the case in part
(a)), and suggests a transition diverging angle of 45º. Will this new diverging angle
achieve the required reduction in pressure loss? Justify your answer.
d) For a transition diverging angle of 90º, the pressure loss is found by a designer to
be higher than for an abrupt exit. Verify this result quantitatively, and explain why
reducing the angle of divergence increases the pressure loss relative to that for an
abrupt exit for this case.
table 12-9b from the heating, ventilating, and air conditioning textbook, sixth edition by faye c. mcquiston
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