One liter of $$20 ^ { \circ } \mathrm { C }$$ C water is collected from a 60-cm-long, 4-mm-diameter tube over a time span of 4 minutes. The length of the entrance region is nearest:
A) 15 cm
B) 25 cm
C) 35 cm
D) 45 cm

Question

Quizplus · Accepted Answer

$34 \mathrm {~cm}$
$\text {Calculate the average velocity and then the Reynolds number:}$
$$V = \frac { V / \mathrm { A } } { \Delta t } = \frac { 0.001 / \left( \pi \times 0.002 ^ { 2 } \right) } { 4 \times 60 } = 0.332 \mathrm {~m} / \mathrm { s } . \quad \operatorname { Re } = \frac { V D } { v } = \frac { 0.332 \times 0.004 } { 10 ^ { - 6 } } = 1330$$
$\text {Obviously this is a laminar flow since $\operatorname { Re } < 2000$. So, the entrance length is}$
$$L _ { E } = 0.065 \operatorname { Re } \times D = 0.065 \times 1330 \times 0.004 = 0.345 \mathrm {~m} \text { or } \underline { 34.5 \mathrm {~cm} }$$
$\text {The entrance region could not be ignored is this tube since it is over half the length of }$$\text {the tube. Most often the entrance region is short compared to the length of a pipe and}$$\text { is ignored. But, in certain situations, possibly in heat exchangers, it cannot be}$$\text { neglected.}$

One Liter Of 20∘C20 ^ { \circ } \mathrm { C }20∘C

One Liter Of $20 ^ { \circ } \mathrm { C }$