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)

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