A gas flows through a square conduit. At one point along the conduit, the conduit sides are 0.1 m, velocity is 7.55 m/sec and mass density of gas is $1.09 k g / m^{3}$ . At a second point, the conduit sides are 0.25 m, velocity is 2.02 m/sec. The mass flow rate and density at second point respectively are:

0.0823 k g / s e c, 1.62 k g / m^{3}

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0.0823 k g / s e c, 0.65 k g / m^{3}

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0.823 k g / s e c, 0.65 k g / m^{3}

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0.823 k g / s e c, 1.62 k g / m^{3}

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Solution

The correct option is B $0.0823 k g / s e c, 0.65 k g / m^{3}$
$Mass flow rate, Q = ρ_{1} A_{1} V_{1}$

$= 1.09 \times (0.1)^{2} \times 7.55$

$= 0.0823 k g / s e c$

Now from conservation of mass principle

$ρ_{1} A_{1} V_{1} = ρ_{2} A_{2} V_{2}$

$0.0823 = ρ_{2} \times (0.25)^{2} \times 2.02$

$ρ_{2} = 0.652 k g / m^{3}$

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