Consider following equation of Bernouilli’s theorem. P + frac{1}{2}ρ {V^2} + ρ gh = K (const

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1.Units, Dimensions and Measurement

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Consider the following equation of Bernouilli’s theorem. $P + \frac{1}{2}\rho {V^2} + \rho gh = K$ (constant)The dimensions of $K/P$ are same as that of which of the following

A

Thrust

B

Pressure

C

Angle

D

Viscosity

Solution

(c) $P+\frac{1}{2} \rho \nu^{2}+\rho g h=K$ (constant)

So, according to principle of homogeneity,

Dimensions of $\mathrm{K}=$ Dimensions of $\mathrm{P}$

$\therefore \frac{K}{P}$ will be dimensionless,

Thus, dimensions of $\frac{K}{P}$ will be same as that of angle (because angle is also dimensinoless quantity),

Standard 11

Physics

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