GATE Mechanical Engineering (ME) 2020 Shift 2 Solved Paper

Question : 62 of 65

Marks: +1, -0

Consider a flow through a nozzle, as shown in the figure below.

The air flow is steady, incompressible and inviscid. The density of air is

1.23 {kg} {/} {m}^{3}

. The pressure difference,

( {p}_{1}

- patm

)

{kPa}

(round off to 2 decimal places).

Solution:

Applying Bernoulli equation

\;{ {P}_{1}}/{ρ g}+\;{ {V}_{1}^{2}}/{2 {g}}+ {z}_{1}=\;{ {P}_{2}}/{ρ {g}}+\;{ {V}_{2}^{2}}/{2 {g}}+ {z}_{2}+ {h}_{ {L}}

(neglect loss of head due to friction)

\;{P_{1}}/{ρ g}+\;{V_{1}^{2}}/{2 g}=\;{P_{a t m}}/{ρ g}+\;{V_{2}^{2}}/{2 g}

(P_{1}-P_{a t m})=ρ \;{(V_{2}^{2}-V_{1}^{2})}/{2}=\;{1}/{2} × 1.23 ×(50^{2}-5^{2})

\;\; =1.522 {kPa}

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