GATE Mechanical Engineering (ME) 2018 Shift 1 Solved Paper

Question : 48 of 65

Marks: +1, -0

Steam flows through a nozzle at mass flow rate of

m=0.1 {kg} {/} {s}

with a heat loss of

5 {kW}

. The enthalpies at inlet and exit are

2500 {kJ} {/} {kg}

and

2350 {kJ} {/} {kg}

, respectively. Assuming negligible velocity at inlet

(C_{1} ≈ 0)

, the velocity

(C_{2})

of steam (in

{m} {/} {s})

at the nozzle exit is ___________ (correct to two decimal places)

Solution:

m=0.1 {kg} \/ {s}, Q=5 {kW}

(heat loss)
Applying SFEE

m(h_{1}+\;{1}/{2} c_{1}^{2}+g z_{1})+Q=m(h_{2}+\;{1}/{2} c_{2}^{2}+g z_{2})+w_{a}

c_{1}=0

and

w_{c v}=0

z_{1}=z_{2}

(assume)

m h_{1}+Q=m h_{2}+m \;{1}/{2} c_{2}^{2}

⇒ 0.1 × \;{1}/{2} c_{2}^{2} × 10^{-3}=0.1(2500-2350)-5

c_{2}=447.213 {m} {/} {s}

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