Consider the following equation of Bernoulli's theorem. P+(1/2) ρ v2+ρ g h=K text (constant) The dimensions of K / P are same as that of which of the following ?

Question

Consider the following equation of Bernoulli's theorem. P+(1/2) ρ v2+ρ 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

Tardigrade Admin · Accepted Answer

P+(1/2) ρ v2+ρ g h=K (constant) So, according to principle of homogeneity, Dimensions of K= Dimensions of P ∴ (K/P) will be dimensionless, Thus, dimensions of (K/P) will be same as that of angle (because angle is also dimensinoless quantity).

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

Thrust

Pressure

Angle

Viscosity

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

Q. Consider the following equation of Bernoulli's theorem. P+21​ρv2+ρgh=K (constant) The dimensions of K/P are same as that of which of the following ?