Question

Consider water flowing through a cylindrical pipe with a variable cross-section. The velocity is v at a point where the pipe diameter is 1.0 cm. At a point where the pipe diameter is three times larger, the velocity is:

nine times larger than the initial velocity
one ninth the initial velocity
three times larger than the initial velocity
the same as the initial velocity
one third the initial velocity

Answer 1

one ninth

Step-by-step explanation:

d = 1 cm , v = v

D = 3d, V = ?

By the equation of continuity,

A V = a v

3.14 x D^2 / 4 x V = 3.14 x d^2 / 4 x v

9d^2 x V = d^2 x v

V = v / 9

Thus, the velocity becomes one ninth the initial velocity