In a laminar flow of a Newtonian fluid through a circular pipe of radius 5 cm, the maximum velocity is found to be 2 m/s. The velocity (in m/s) at a radial distance of 2.50 cm from the axis of the pipe is

The correct option is 1.50.

Detailed Explanation:

For the steady, laminar flow of a Newtonian fluid through a circular pipe (also known as Hagen-Poiseuille flow), the velocity distribution across the cross-section of the pipe is parabolic. The velocity at any radial distance $r$ from the central axis of the pipe is given by the following relation:

$$u\left(r\right)=u_{\max }[1-{\left(\frac{r}{R}\right)}^2]$$

Where:
- $u\left(r\right)$ is the velocity of the fluid at a radial distance $r$ from the axis.
- $u_{\max }$ is the maximum velocity of the fluid, which occurs at the center of the pipe ($r=0$).
- $R$ is the total radius of the circular pipe.
- $r$ is the radial distance from the central axis of the pipe where the velocity needs to be calculated.

Given data from the problem:
- Radius of the pipe, $R=5\text{cm}$
- Maximum velocity, $u_{\max }=2\text{m/s}$
- Radial distance, $r=2.50\text{cm}$

Now, we substitute these values into the velocity profile formula:

$$u\left(2.50\right)=2\times [1-{\left(\frac{2.50}{5}\right)}^2]$$

Simplify the ratio inside the parentheses:

$$\frac{2.50}{5}=0.5$$

Substitute this value back into the equation:

$$u\left(2.50\right)=2\times [1-{\left(0.5\right)}^2]$$

Calculate the square of 0.5:

$${\left(0.5\right)}^2=0.25$$

Perform the subtraction inside the bracket:

$$1-0.25=0.75$$

Multiply by the maximum velocity to find the final velocity:

$$u\left(2.50\right)=2\times 0.75=1.50\text{m/s}$$

Thus, the velocity of the fluid at a radial distance of 2.50 cm from the axis of the pipe is 1.50 m/s.