The equation (7.3.20) for the head loss is valid for both laminar and turbulent flows. We wish to pump the flow rate Q through a long pipe of diameter D, to be selected. The head loss is
Proportional to what power of D, assuming a constant friction factor?
A) $D ^ { - 2 }$
B) $D ^ { - 3 }$
C) $D ^ { - 4 }$
D) $D ^ { - 5 }$

Question

The equation (7.3.20) for the head loss is valid for both laminar and turbulent flows. We wish to pump the flow rate Q through a long pipe of diameter D, to be selected. The head loss is
Proportional to what power of D, assuming a constant friction factor? 
A) $D ^ { - 2 }$
B) $D ^ { - 3 }$
C) $D ^ { - 4 }$
D) $D ^ { - 5 }$

Quizplus · Accepted Answer

$D ^ { - 5 }$
$\text {Write Eq. 7.3.20 in terms of $D$ :}$
$$h _ { L } = f \frac { L } { D } \frac { V ^ { 2 } } { 2 g } = f \frac { L } { D } \frac { Q ^ { 2 } / A ^ { 2 } } { 2 g } = f \frac { L } { D } \frac { Q ^ { 2 } } { \left( \pi D ^ { 2 } / 4 \right) ^ { 2 } 2 g } = f \frac { L } { D ^ { 5 } } \frac { 8 Q ^ { 2 } } { \pi ^ { 2 } g }$$
$\text {The head loss is proportional to $D ^ { - 5 }$.}$

The Equation (7 D−2D ^ { - 2 }D−2 B) D−3D ^ { - 3 }D−3

The Equation (7 $D ^ { - 2 }$ B) $D ^ { - 3 }$