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

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the equation is dimensionally correct

if dimensions of $u_{0} are [M^{0} {LT}^{0}]$ the equation is dimensionally correct

dimensions of $\frac{p}{ρg}$ are same as that of $\frac{v^{2}}{2 g}$

none of the above

answer is A, B, C.

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Detailed Solution

$Dimensions of [\frac{p}{ρg}] = dimensions of [\frac{v^{2}}{2 g}]$

$= dimensions of h = dimensions of u_{0}$

$∴ Dimensions of μ_{0} = [M^{0} {LT}^{0}]$

Hence, options(1),(2) and (3) are correct.

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