Question

Check the dimensional consistency of Fx = Pv

Answer 1

To check:

Dimensional consistency of the given equation:

(Fx = Pv)

Solution:

For DIMENSIONAL ANALYSIS , we need to separately check the dimensions of the quantities on LHS AND RHS and check their consistency.

LHS:

$\therefore \: \bigg \{F \times x \bigg \} = \bigg \{force \times displacement \bigg \}$

$\implies\: \bigg \{F \times x \bigg \} = \bigg \{ ML{T}^{ - 2} \times L \bigg \}$

$\implies\: \bigg \{F \times x \bigg \} = \bigg \{ M{L}^{2} {T}^{ - 2} \bigg \}$

RHS:

$\therefore \: \bigg \{P \times v \bigg \} = \bigg \{pressure \times velocity\bigg \}$

$\implies\: \bigg \{P \times v \bigg \} = \bigg \{ M{L}^{ - 1} {T}^{ - 2} \times L{T}^{ - 1} \bigg \}$

$\implies\: \bigg \{P \times v \bigg \} = \bigg \{ M{L}^{0} {T}^{ - 3}\bigg \}$

$\boxed{ \bold{ \therefore \: LHS \: \neq \: RHS}}$

Hence , the equation is dimensionally inconsistent.