Basic Mechanical Engineering (3110006)

Question-4c-OR

BE | Semester-1 Summer-2019 | 04-06-2023

Q4) (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

p_{m} = 5 bar = 500 kPa

N = 1000 rpm

γ = 1.4

Find:

η_{rel} = ?

I . P . = ?

Solution:

Now,

r = compression ratio = \frac{V_{s} + V_{c}}{V_{c}}

r = \frac{(\frac{π}{4} \times 0 . 15^{2} \times 0.2) + (7 \times 10^{- 4})}{7 \times 10^{- 4}}

r = 6.049

Now, the air standard efficiency is given by,

η_{air} = 1 - \frac{1}{{(r)}^{γ - 1}}

η_{air} = 1 - \frac{1}{{(6.049)}^{1.4 - 1}}

η_{air} = 0.5131

Now, the relative efficiency is given by,

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

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

η_{rel} = 58.82 %

Now, Indicated power is given by,

I . P . = \frac{p_{m} L A N}{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