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Conservation of Energy

A small steam...

Question

A small steam whistle (perfectly insulated and doing no shaft work) causes a drop of 0.8 kJ/kg in emthalpy of steam from entry to exit. If the kinetic energy of the steam at entry is negligible, the velocity of the steam at exit is

A

4 m/s

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B

40 m/s

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C

80 m/s

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D

120 m/s

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Solution

The correct option is B 40 m/s
(b)
Given data:
$Δ h = - 0.8 k J / k g$
$h_{2} - h_{1} = - 0.8 k J / k g$
$h_{1} - h_{2} = 0.8 k J / k g$
Applying steady flow energy equation,
$h_{1} + \frac{V_{1}^{2}}{2} + g z_{1} + q = h_{2} + \frac{V_{1}^{2}}{2} + g z_{2} + w$
Assumption:
(i) $q = 0$ adiabatic flow
(ii) $w = 0$
(iii) Change K.E. and P.E are neglect
(iv) Neglect inlet velocity.
$∴$ $h_{1} = h_{2} + \frac{V_{2}^{2}}{2}$
$h_{1} = h_{2} + \frac{V_{2}^{2}}{2000}$
$h_{1} - h_{2} = \frac{V_{2}^{2}}{2000}$
or $8 = \frac{V_{2}^{2}}{2000}$
$V_{2}^{2} = 1600 o r V_{2} = 40 m / s$

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