Consider a modified Bernoulli equation.

$(P + \frac{A}{B t^{2}}) + ρ g (h + B t) + \frac{1}{2} ρ v^{2} = constant .$

If t has the dimension of time then the dimensions of A and B are ________, ________ respectively. [2026]

Question

Consider a modified Bernoulli equation.

$(P + \frac{A}{B t^{2}}) + ρ g (h + B t) + \frac{1}{2} ρ v^{2} = constant .$

If t has the dimension of time then the dimensions of A and B are ________, ________ respectively. [2026]

Smart Achievers · Accepted Answer

(1)

$\Rightarrow [P] = [\frac{A}{B t^{2}}] . . . . . (1)$

$\Rightarrow [h] = [B t] . . . . . (2)$

$\Rightarrow [B] = [\frac{h}{t}] = [\frac{L}{T}] = [L T^{- 1}]$

$Putting B in equation (1)$

$[M L^{- 1} T^{- 2}] = [\frac{A}{L T^{- 1} \times T^{2}}]$

$[A] = [M L^{0} T^{- 1}]$

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