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Document Title
Fundamentals of Stress and Vibration 2. Engineering Mechanics Chapter
[A Practical guide for aspiring Designers / Analysts]

Since (x = 1), we have (z = 2)

2
This given us the relationship: s = at - - - - (2.3)
It is to be noted that, the actual relationship between displacement, acceleration and time, for a
straight line motion, is given by:

1
2
s = at
2
The limitation of this approach is that, the constant (1/2) cannot be computed.

šƒ’Ž‡ ʹǣ ‹– ƒ „‡ ƒ”‰—‡† ‘‘•‡•‹ ƒŽŽ› –Šƒ–ǡ –Š‡ –Š”—•– †‡˜‡Ž‘’‡† „› ƒ ™‹†‹ŽŽ
†‡’‡†• ‘ ™‹† ˜‡Ž‘ ‹–›ǡ †‡•‹–› ‘ˆ –Š‡ ƒ‹”ǡ ‰‡‘‡–”› ‘ˆ –Š‡ ƒ‡”‘ ˆ‘‹Ž ȋ”ƒ†‹—• ‘ˆ –Š‡ ƒ‡”‘ ˆ‘‹ŽȌ ƒ†
‘ˆ –Š‡ ™‹†‹ŽŽǤ

a b
c d
Mathematically, thrust is given by: T = v ρ N r - - - - (2.4)
Š‡”‡ǡ ȋƒǡ „ǡ ƒ† †Ȍ ƒ”‡ ‡š’‘‡–• ‘ˆ –Š‡‹” ”‡•’‡ –‹˜‡ –‡”•Ǥ

Parameters Units Dimensions

Thrust (T) Newton (N) Mass ∗ Acceleration(MLT −2 )

m −1
Velocity (v) meter/second Length/time LT
s

−3
kg Mass/Volume ML
Density (ρ) kilogram/meter
3
m 3
Radius (r) Meters (m) Length (L)

1 (T −1 )
RPS (N) revolutions/second
s

Writing the dimension of parameters in equation (2.4), we get:

b
c d
a b
L = MLT
ML T
T = v ρ N r = MLT −2 = LT −2 a 3 b −1 c d −2 = L a+d−3b T −a−c M - - - - (2.5)
By equating the exponents of the respective dimensions of LHS and RHS from equation (2.5), we get:
(b = 1) : exponents of mass (M)
(a + c = 2) : exponents of time (T)

(a + d – 3b = 1) : exponents of length (L)

QP No. SSC/Q4401, Version 1.0, NSQF Level 7, Compliant with Aero and Auto Industries, P
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