| Water flows out from a beaker through a capillary of length 200 mm and diameter 2 mm. |
 |
| Density of water is \[1000\,kg\,{{m}^{-\,3}}\]and its viscosity is 0.8 centipoise. If a level of 5 cm is continuously maintained in the beaker, then flow rate through capillary is nearly |
A) \[5\,mL{{s}^{-1}}\]
B) \[1\,\,mL{{s}^{-1}}\]
C) \[15\,mL{{s}^{-1}}\]
D) \[13\,\,mL{{s}^{-1}}\]
Correct Answer: B
Solution :
| Pressure differential across capillary is \[{{p}_{i}}-{{p}_{o}}=\rho gh\] |
| \[=1000\times 10\times 0.05\] |
| \[=5000N{{m}^{-\,2}}\] |
| Viscosity of water is \[\eta =\left( 0.8cp\times \frac{{{10}^{-\,3}}}{cp}Kg{{m}^{-1}}{{s}^{-\,1}} \right)\] |
| \[=8\times {{10}^{-\,4}}kg{{m}^{-1}}{{s}^{-1}}\] |
| Flow rate using Poiseuille's law is |
| \[j=\frac{\pi {{r}^{4}}({{p}_{i}}-{{p}_{o}})}{8\eta L}\] |
| \[=\frac{\pi \times 1\times {{10}^{-\,4}}\times 5000}{8\times 8\times {{10}^{-\,4}}\times 0.2}\] |
| \[=\frac{5\pi }{128}\times {{10}^{-\,5}}{{m}^{3}}{{s}^{-1}}\approx 1.0\,mL{{s}^{-\,1}}\] |
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