Question

Water flows in a streamlined manner through a capillary tube of radius a, the pressure difference being P and the rate of flow Q. If the radius is reduced to a/2 and the pressure increased to 2P, the rate of flow becomes

• A. (a) $4 Q$
• A. (b) Q
• A. (c)
• A. (d) $\frac { Q } { 8 }$

Answer 1

(d)

Sol. $\eta$ and $l$ are constants)

∴ $\frac { V _ { 2 } } { V _ { 1 } } = \left( \frac { P _ { 2 } } { P _ { 1 } } \right) \left( \frac { r _ { 2 } } { r _ { 1 } } \right) ^ { 4 }$= $\frac { 1 } { 8 }$∴ $V _ { 2 } = \frac { Q } { 8 }$