Solve Q = (\pi * D^2 * n * H) / (4 * g)

Evaluate

Q = \frac{π D ^{2} n H}{4 g}

Rewrite the expression

Q = \frac{πn H D ^{2}}{4 g}

Swap the sides of the equation

\frac{πn H D ^{2}}{4 g} = Q

Cross multiply

πn H D^{2} = 4 g Q

Divide both sides

\frac{πn H D ^{2}}{πn H} = \frac{4 g Q}{πn H}

Divide the numbers

D^{2} = \frac{4 g Q}{πn H}

Take the root of both sides of the equation and remember to use both positive and negative roots

D = \pm \frac{4 g Q}{πn H}

Simplify the expression

More Steps

D = \pm \frac{4 π g Q n H}{π ∣ n H ∣}

Separate the equation into 2 possible cases

D = \frac{4 π g Q n H}{π ∣ n H ∣} D = - \frac{4 π g Q n H}{π ∣ n H ∣}

Simplify

D = \frac{2 π H n Q g}{π ∣ n H ∣} D = - \frac{4 π g Q n H}{π ∣ n H ∣}

Solution

D = \frac{2 π H n Q g}{π ∣ n H ∣} D = - \frac{2 π H n Q g}{π ∣ n H ∣}

Q = (\pi * d^2 * n * h) / (4 * g)