Question

If $p, \rho, g$ and $h$ denote pressure, density, acceleration due to gravity and height, respectively. In the case of flow of fluid, $\frac{p}{\rho g}+\frac{v^{2}}{2 g}+h=u_{0}$, where $v$ denotes velocity. Mark the correct option(s).

• A. the equation is dimensionally correct
• B. if dimensions of $u_{0}$ are $\left[M^{0} L T^{0}\right]$, the equation is dimensionally correct
• C. dimensions of $\frac{p}{\rho g}$ are same as that of $\frac{v^{2}}{2 g}$
• D. none of the above

Answer 1

Answer: (B), (C)

Dimensions of $\left[\frac{p}{\rho g}\right]=$ dimensions of $\left[\frac{v^{2}}{2 g}\right]$
$=$ dimensions of $h=$ dimensions of $u_{0}$.
$\therefore$ Dimensions of $\mu_{0}=\left[M^{0} L T^{0}\right]$