Question

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

• A. Thrust
• B. Pressure
• C. Angle
• D. Viscosity

Answer 1

Answer: (C)

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