Question

A system has fundamental quantities as
density [D], velocity [V] and area [A]. The
dimensional representation of power in this
system is​

Answer 1

Answer:

F=DxVyAz

Equate power of dimensions.

[AV2D]

is correct answer

thank you

Answer 2

Concept:

• Dimensional analysis
• Representing Power in terms of density, velocity and area
• Understanding the units of various physical quantities

Given:

• Density D= [M/L^3]
• Velocity V = [L/T]
• Area A = [L^2]

Find:

• Dimensional representation of power in terms of density, velocity and area

Solution:

Let the dimensional representation of power in terms of density, velocity and area be P = D^a V^b A^c

P = [M/L^3]^a [L/T]^b [L^2]^c

P = [M^a/L^3a] [L^b /T^b ] [L^2c]

P = [M^a L^(b-3a+2c) T^-b]

We know the dimensions of power

P = [ML^2T^-3]

[ML^2T^-3] = [M^a L^(b-3a+2c) T^-b]

On comparison,

a = 1

b-3a+2c = 2

-b = -3

b = 3

3-3(1) +2c = 2

c = 1

Therefore, a = 1, b = 3, c = 1

The dimensional representation of power is P = [D V^3 A].

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