Solve {l}{Q=k*sqrt{DeltaP}}{k=0.87*A}{A=pid^2}{d=10}{Q=20}

$$\left. \begin{array} { l } { Q = k \cdot \sqrt { \Delta P } } \\ { k = 0.87 \cdot A } \\ { A = \pi d ^ { 2 } } \\ { d = 10 } \\ { Q = 20 } \end{array} \right.$$

Solve for Q, k, Δ, P, A, d (complex solution)

$$Q=87\pi \sqrt{P\Delta }$$

$$k=87\pi \approx 273.318560862$$

$$\Delta \in \mathrm{C}$$

$$P\in \mathrm{C}$$

$$A=100\pi \approx 314.159265359$$

$$d=10$$

Solve for Q, k, Δ, P, A, d

$$\left\{\begin{matrix}\\Q=0\text{, }k=87\pi \approx 273.318560862\text{, }\Delta =0\text{, }P\leq 0\text{, }A=100\pi \approx 314.159265359\text{, }d=10\text{; }Q=0\text{, }k=87\pi \approx 273.318560862\text{, }\Delta =0\text{, }P\geq 0\text{, }A=100\pi \approx 314.159265359\text{, }d=10\text{; }Q=87\pi \sqrt{P\Delta }\text{, }k=87\pi \approx 273.318560862\text{, }\Delta =0\text{, }P\leq 0\text{, }A=100\pi \approx 314.159265359\text{, }d=10\text{; }Q=87\pi \sqrt{P\Delta }\text{, }k=87\pi \approx 273.318560862\text{, }\Delta =0\text{, }P\geq 0\text{, }A=100\pi \approx 314.159265359\text{, }d=10\text{, }&\text{unconditionally}\\Q=87\pi \sqrt{P\Delta }\text{, }k=87\pi \approx 273.318560862\text{, }\Delta \leq 0\text{, }P\leq 0\text{, }A=100\pi \approx 314.159265359\text{, }d=10\text{, }&P\leq 0\\Q=87\pi \sqrt{P\Delta }\text{, }k=87\pi \approx 273.318560862\text{, }\Delta \geq 0\text{, }P\geq 0\text{, }A=100\pi \approx 314.159265359\text{, }d=10\text{, }&P\geq 0\end{matrix}\right.$$