Question

Water flows through a horizontal pipe. The diameter of the pipe at point b is larger than the diameter of the pipe at point
a. Where is the speed of the water the greatest?

Answer 1

Answer:

At point A

Explanation:

As we know

Velocity is inversely proportional to Area of cross section

so, at point A area is small so velocity will be high

Answer 2

1. From law of conservation of mass

Rate of mass of fluid entering at inlet =Rate of mass of fluid  exit at outlet

2. But here fluid is water which is in-compressible fluid, so we can write above equation

So

Volume flow rate of water at inlet=Volume flow rate of water at inlet

3. Where

Volume flow rate=Cross sectional area of pipe×Velocity of fluid at that instant

Q= A×V

$\mathbf{V=\frac{Q}{A}}$    ...1)

4. From above relation, we see that for a constant value of flow rate(Q)

Velocity is inversely proportional to cross- sectional area of pipe.

Where area of pipe is directly proportional to square of diameter of pipe.

Means

Velocity is inversely proportional to square of diameter of pipe.

5. So

Velocity of water is higher for smaller diameter of pipe.

And velocity is lower for larger for larger diameter of pipe.

So velocity of water is larger at point A compare to point B because diameter of pipe at point A is smaller to point B.