A pressure drop of 200 kPa is measured over a 50-m-length of 2-mm-diameter pipe trans- porting 30 $$30 ^ { \circ } \mathrm { C }$$ C water. If a laminar flow exists, the flow rate is nearest:
A) 0.00195 L/s
B) 0.00243 L/s
C) 0.00732 L/s
D) 0.00991 L/s

Question

Quizplus · Accepted Answer

$0.00195 \mathrm {~L} / \mathrm { s }$
$\text {Use Eq. 7.3.20:}$
$$\frac { 200000 } { 9810 } = \frac { 64 \times \left( 0.804 \times 10 ^ { - 6 } \right) } { V \times 0.002 } \frac { 50 } { 0.002 } \frac { V ^ { 2 } } { 2 \times 9.81 } . \quad \therefore V = 0.622 \mathrm {~m} / \mathrm { s }$$
$\text {The flow rate is then}$
$$Q = A V = \pi \times 0.001 ^ { 2 } \times 0.622 = \underline { 1.95 \times 10 ^ { - 6 } \mathrm {~m} ^ { 3 } / \mathrm { s } } \text { or } \underline { 0.00195 \mathrm {~L} / \mathrm { s } }$$
$\text {Check the Reynolds number to make sure the flow is laminar:}$
$$\operatorname { Re } = \frac { V D } { v } = \frac { 0.622 \times 0.002 } { 0.804 \times 10 ^ { - 6 } } = 1550 . \quad \therefore \text { Laminar }$$
$\text {The diameters of most pipes of engineering interest are not this small so laminar }$$\text {flow is seldom of interest.}$

A Pressure Drop of 200 KPa Is Measured Over a 50-M-Length