Question

Water is conveyed through a uniform tube of 8cm in diameter and 3140m in length at the rate of $2\times {10}^{-3}{m}^3$ per second. The pressure required to maintain the flow is (viscosity of water $=$ 10${}^{-3}$ S.I. units):

• A. 6.25 Nm${}^{-2}$
• B. 0.625 Nm${}^{-2}$
• C. 6250 Nm${}^{-2}$
• D. 0.00625 Nm${}^{-2}$

Answer 1

The correct option is C 6250 Nm${}^{-2}$

Given that,

Radius of tube ,$r=4cm=0.04m$

Length of tube ,$L=3140m$

Viscosity of water, $\eta ={10}^{-3}$ S.I. units

Flow rate of water through tube, $Q=2\times {10}^{-3}{m}^3$

According to poiseullie's equation,

$Q=\frac{\pi P{r}^4}{8\eta L}$

$P=\frac{2\times {10}^{-3}\times 8\times {10}^{-3}\times 3140}{3.14\times {0.04}^4}=6250N{m}^{-2}$

$\therefore$ Presure required to maintain the flow ,$P=6250N{m}^{-2}$