What are the dimensional units of $A$ and $B$ if a volume, $V$ , is given by the equation $V=A*t^3+B/t$ ?

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Answer 1 · 2016-03-19T10:31:17

$A$ is $L^3/T^3$ and $B$ is $L^3*T$

Any volume can be expressed as cubic length, $L^3$

Only adding up cubic lengths on the right will give the result of another cubic length on the left (Note: multiplying terms would not do this).

So, given $V=A*T^3+B/T$ , let

$A*T^3=L^3$ meaning the first term is a volume (cubic length), and
$B/T = L^3$ meaning the second term is also a volume.

Finally we just solve for the respective letters, $A$ and $B$ .

$A=L^3/T^3$
$B=L^3*T$

What are the dimensional units of AA and BB if a volume, VV, is given by the equation V=A*t^3+B/tV=A*t^3+B/t?