Question

3. If a pipe with flowing water has a cross-sectional area nine times greater at point 2 than at point 1, what would be the relation of flow speed at the two points?

Answer 1

Answer:

The velocity of the flow at point 1 is nine times greater than the velocity at point 2.

Explanation:

We know that the same volume of water entering through point 1 must exit through point 2.

The volume of water per unit of time or the volumetric flow is defined by:

$V_{flow}=v*A\\ where:\\V_{flow}= flow [m^3/s]\\v=velocity[m/s]\\A=area [m^2]$

If  $A_{2}=9*A_{1}$

therefore

$v_{1} *A_{1} = v_{2} *A_{2} \\v_{1} *A_{1} = v_{2} *9A_{1} \\\\v_{1} = 9v_{2}$