Consider again Example C.1.2 . A hole 6 mm in diameter was made in a translucent milk container (Figure C.1.7). A series of marks 1 cm apart was made above the hole. While adjusting the tap flow to keep the water height constant, the time for the outflow to fill a 250 ml cup was measured (1 ml = 10[latex]^{−6}[/latex] m³). This was repeated for several heights. The data are given in the following table. [latex]\begin{array}{l|lllllllllll}\text{Height} h( cm ) & 11 & 10 & 9 & 8 & 7 & 6 & 5 & 4 & 3 & 2 & 1 \\\hline \text{Time} t( s ) & 7 & 7.5 & 8 & 8.5 & 9 & 9.5 & 11 & 12 & 14 & 19 & 26\end{array}[/latex] Obtain a functional description of the volume outflow rate f as a function of water height h above the hole.

First obtain the flow rate data in ml/s by dividing the 250 ml volume by the time to fill: [latex]f=\frac{250}{t}[/latex] (1) In Example C.1.2 , we learned that the following power function can describe the data: [latex]f=b h^m[/latex] (2)

Question C.3.5: Consider again Example C.1.2. A hole 6 mm in diameter was ma...

System Dynamics

Consider again Example C.1.2. A hole 6 mm in diameter was made in a translucent milk container (Figure C.1.7). A series of marks 1 cm apart was made above the hole. While adjusting the tap flow to keep the water height constant, the time for the outflow to fill a 250 ml cup was measured (1 ml = 10 $^{−6}$ m³). This was repeated for several heights. The data are given in the following table.

$\begin{array}{l|lllllllllll}\text{Height} h( cm ) & 11 & 10 & 9 & 8 & 7 & 6 & 5 & 4 & 3 & 2 & 1 \\\hline \text{Time} t( s ) & 7 & 7.5 & 8 & 8.5 & 9 & 9.5 & 11 & 12 & 14 & 19 & 26\end{array}$

Obtain a functional description of the volume outflow rate f as a function of water height h above the hole.

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