Question

The volume of a liquid $\left(V\right)$ that passes a given cross- section area $\left(A\right)$ in a given time $\left(t\right)$ depends on velocity of flow $\left(u\right),A$ and $t$ as $V=u^a{A}^b{t}^c$ then:

• A. $a=0,b=1,c=1$
• B. $a=1,b=-1,c=1$
• C. $a=1,b=1,c=1$
• D. $a=-1,b=-1,c=-1$

Answer 1

Answer: (C)

$V={\left[u\right]}^a{\left[A\right]}^b{\left[T\right]}^c$
$\left[L^3\right]={\left[M^{0}L{T}^{-1}\right]}^a{\left[M^0{L}^2\right]}^b{\left[M^{0}T\right]}^c$
$a+2b=3,-a+c=0$
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