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Aspect ratio of rectangular duct is 7 and its equivalent circular duct diameter is 100 mm. The ratio of longer side of rectangular duct to the diameter of circular duct is 2.6.

find the dimension of shorter side of duct.

Mumbai University > Mechanical Engineering > Sem 8 > Refrigeration and air conditioning

Marks: 06M

Year: Dec 2016

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The given data is

$\frac{b}{a}=7 and \frac{b}{D}=2.6$

For the given condition, the relation between the two geometric sections is given by

D=1.256$[\frac{ab{^3}}{(a+b)}]^{(1/5)}$

substituting the given values

10=$1.265[\frac{(a×7a)^3}{8a}]^{(1/5)}=1.265×a(\frac{343}{8})^{0.2}=2.68a$

∴a=10/2.68=3.73 cm

b=7×3.73=26.12 cm

as $\frac{b}{D}=\frac{26.2}{10}$=2.61 which satisfes the third given condition

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28views

The given data is

$\frac{b}{a}=7 and \frac{b}{D}=2.6$

For the given condition, the relation between the two geometric sections is given by

D=1.256$[\frac{ab{^3}}{(a+b)}]^{(1/5)}$

substituting the given values

10=$1.265[\frac{(a×7a)^3}{8a}]^{(1/5)}=1.265×a(\frac{343}{8})^{0.2}=2.68a$

∴a=10/2.68=3.73 cm

b=7×3.73=26.12 cm

as $\frac{b}{D}=\frac{26.2}{10}$=2.61 which satisfes the third given condition

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15views

The given data is

$\frac{b}{a}=7 and \frac{b}{D}=2.6$

For the given condition, the relation between the two geometric sections is given by

D=1.256$[\frac{ab{^3}}{(a+b)}]^{(1/5)}$

substituting the given values

10=$1.265[\frac{(a×7a)^3}{8a}]^{(1/5)}=1.265×a(\frac{343}{8})^{0.2}=2.68a$

∴a=10/2.68=3.73 cm

b=7×3.73=26.12 cm

as $\frac{b}{D}=\frac{26.2}{10}$=2.61 which satisfes the third given condition