Basic Mechanical Engineering (3110006)

Question-3c-OR

BE | Semester-1 Summer-2020 | 11-06-2020

Q3) (c)

Given data:

L = 0.2 m

d = 0.15 m

V_{C} = 7 \times 10^{5} {mm}^{3} = 7 \times 10^{- 4} m^{3}

η_{ith} = 0.30 bar

p_{m} = 5 bar = 500 kPa

N = 100 rpm

γ = 1.4

Find:

η_{rel} = ?

I . P . = ?

Solution:

The relative efficiency is givne by

η_{rel} = \frac{η_{ith}}{η_{air}} \times 100 %

But, the air standard efficiency is given by,

η_{air} = 1 - \frac{1}{{(r)}^{γ - 1}}

Where,

r = compression ratio = \frac{V_{s} + V_{c}}{V_{c}} = \frac{(\frac{π}{4} \times 0 . 15^{2} \times 0.2) + (7 \times 10^{- 4})}{7 \times 10^{- 4}} = 6.046

Now,

η_{air} = 1 - \frac{1}{{(6.046)}^{1.4 - 1}} = 0.5131

Thus,

η_{rel} = \frac{0.30}{0.51} \times 100 % = 58.82 %

Indicated power is given by,

I . P . = \frac{p_{m} LAN}{60 \times 2} \times no . of cylinder, kW

I . P . = \frac{500 \times 0.2 \times \frac{π}{4} \times 0 . 15^{2} \times 1000}{60 \times 2} \times 1

I . P . = 14.718 kW