Two tanks are connected together in the following unusual

Step 1 of 4

Refer to figure E2.3 in the text book for the two tank system.

(a)

Write the mass balance equation for the tank system.

\(\rho A_{1} \frac{d h_{1}}{d t}=w_{1}-w_{2}-w_{3}\)

Here, 

\(A_{1}\) is the area of cross section of tank 1

\(h_{1}\) is the height of water in tank 1

\(w_{1}\), \(w_{2}\) and \(w_{3}\) are the mass flow rates

Write the mass equation for the mass variation of the tank 2.

\(\rho A_{2} \frac{d h_{2}}{d t}=w_{2}\)

Here,

\(A_{2}\) is the area across section of tank 2

\(h_{2}\) is the height of water in tank 2

Thus, the model equations of the system are

\(\begin{array}{l}
\rho A_{1} \frac{d h_{1}}{d t}=w_{1}-w_{2}-w_{3} \\
\rho A_{2} \frac{d h_{2}}{d t}=w_{2} \\
w_{2}=\frac{\rho g}{g_{c} R_{2}}\left(h_{1}-h_{2}\right) \\
w_{3}=\frac{\rho g h_{1}}{g_{c} R_{3}}
\end{array}\)