Water flows from point $ A $ to points $ D $ and $ E $ as shown. Some of the flow parameters are known, as shown in the table. Determine the unknown parameters. Note the diagram above does not show the relative diameters of each section of the pipe.

Section
Diameter
Flow Rate
Velocity

$ \text{AB} $
$ 300 $ $ \text{mm} $
$\textbf{?}$
$\textbf{?}$

$ \text{BC} $
$ 600 $ $ \text{mm} $
$\textbf{?}$
$ 1.2 $ $ \text{m/s} $

$ \text{CD} $
$\textbf{?}$
$ Q_{CD} = 2Q_{CE} $ $ \text{m}^3/\text{s} $
$ 1.4 $ $ \text{m/s} $

$ \text{CE} $
$ 150 $ $ \text{mm} $
$ Q_{CE} = 0.5Q_{CD} $ $ \text{m}^3/\text{s} $
$\textbf{?}$

Question

Water flows from point $ A $ to points $ D $ and $ E $ as shown. Some of the flow parameters are known, as shown in the table. Determine the unknown parameters. Note the diagram above does not show the relative diameters of each section of the pipe.

Section
Diameter
Flow Rate
Velocity

$ \text{AB} $
$ 300 $ $ \text{mm} $
 $\textbf{?}$
 $\textbf{?}$

$ \text{BC} $
$ 600 $ $ \text{mm} $
 $\textbf{?}$
$ 1.2 $ $ \text{m/s} $

$ \text{CD} $
 $\textbf{?}$
$ Q_{CD} = 2Q_{CE} $ $ \text{m}^3/\text{s} $
$ 1.4 $ $ \text{m/s} $

$ \text{CE} $
$ 150 $ $ \text{mm} $
$ Q_{CE} = 0.5Q_{CD} $ $ \text{m}^3/\text{s} $
 $\textbf{?}$

Jason · Accepted Answer

$ Q_{AB} = 0.3393 $ $ \text{m}^3/\text{s} $
$ v_{AB} = 4.8 $ $ \text{m/s} $
$ Q_{BC} = 0.3393 $ $ \text{m}^3/\text{s} $
$ d_{CD} = 0.454 $ $ \text{m} $ $ = 454 $ $ \text{mm} $
$ v_{CE} = 6.4 $ $ \text{m/s} $

Section	Diameter	Flow Rate	Velocity
\( \text{AB} \)	\( 300 \) \( \text{mm} \)	\(\textbf{?}\)	\(\textbf{?}\)
\( \text{BC} \)	\( 600 \) \( \text{mm} \)	\(\textbf{?}\)	\( 1.2 \) \( \text{m/s} \)
\( \text{CD} \)	\(\textbf{?}\)	\( Q_{CD} = 2Q_{CE} \) \( \text{m}^3/\text{s} \)	\( 1.4 \) \( \text{m/s} \)
\( \text{CE} \)	\( 150 \) \( \text{mm} \)	\( Q_{CE} = 0.5Q_{CD} \) \( \text{m}^3/\text{s} \)	\(\textbf{?}\)

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