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Question

Physics Question on mechanical properties of fluid

Consider the following equation of Bernoulli's theorem. P+12ρv2+ρgh=K (constant) P+\frac{1}{2} \rho v^{2}+\rho g h=K \text { (constant) } The dimensions of K/PK / P are same as that of which of the following ?

A

Thrust

B

Pressure

C

Angle

D

Viscosity

Answer

Angle

Explanation

Solution

P+12ρv2+ρgh=KP+\frac{1}{2} \rho v^{2}+\rho g h=K (constant) So, according to principle of homogeneity, Dimensions of K=K= Dimensions of PP KP\therefore \frac{K}{P} will be dimensionless, Thus, dimensions of KP\frac{K}{P} will be same as that of angle (because angle is also dimensinoless quantity).