Question

A fluid travels through a pipe of cross-sectional area A1 then moves through a connection into another pipe of cross-sectional area A2. If A1 is larger than A2, the velocity of the fluid will ______.

Group of answer choices

A. increase

B. decrease

C. remain constant

D. evaporate

Answer 1

This question can be solved using The equation of Continuity

which states that if an incompressible fluid flows through

a Pipe then its  Volume must not change

or

Volume of fluid going in through

a pipe must be equal to the volume of Fluid Coming out of the pipe.

This can mathematically be expresses if we have the cross-section area of a pipe to be A

and velocity of fluid through that cross section be v then A*v must be constant.

.

Now,Considering the above question,

Given that,

.

And from equation of continuity we know,

We know,

Multiplying by v1 both sides we get

and from above equation we know,

.

So the velocity of the fluid will increase because .