Reynolds Number and its Significance:
The Reynolds number is a dimensionless quantity used to predict the flow regime of a fluid around a solid object. It helps determine whether the flow is laminar or turbulent. It is defined as the ratio of inertial forces to viscous forces and is given by the formula:

Reynolds number (Re) = (ρvd)/η

where:
- ρ is the density of the fluid
- v is the velocity of the object
- d is the characteristic length of the object
- η is the dynamic viscosity of the fluid

Given Data:
- Radius of the sphere (r) = 15 cm = 0.15 m
- Velocity of the sphere (v) = 2 m/s
- Specific gravity of the liquid (SG) = 0.9
- Dynamic viscosity of the liquid (η) = 0.8 poise = 0.08 Pa.s

Calculating Density:
The density of the liquid can be calculated using the specific gravity formula:

Density of liquid (ρ) = SG * Density of water

Assuming the density of water to be 1000 kg/m³:

ρ = 0.9 * 1000 = 900 kg/m³

Calculating Reynolds Number:
The characteristic length of the sphere is its diameter (2r):

d = 2 * 0.15 = 0.3 m

Substituting the given values into the Reynolds number formula:

Re = (ρ * v * d) / η

Re = (900 * 2 * 0.3) / 0.08

Re = 2700 / 0.08

Re = 33750

Interpreting the Reynolds Number:
The Reynolds number can be used to determine the flow regime around the sphere. Here are the general guidelines:

1. Reynolds Number < 2000:="" laminar="" />
- The fluid flows smoothly in parallel layers with little mixing.
- The flow is predictable and stable.

2. Reynolds Number > 4000: Turbulent Flow
- The fluid flows irregularly with chaotic eddies and mixing.
- The flow is unpredictable and less stable.

3. 2000 < reynolds="" number="" />< 4000:="" transitional="" />
- The flow exhibits characteristics of both laminar and turbulent flow.
- The flow regime may transition between laminar and turbulent.

Conclusion:
In this case, the Reynolds number is calculated to be 33750, which is greater than 4000. Therefore, the flow around the sphere will likely be turbulent. The high Reynolds number indicates that the inertial forces dominate over the viscous forces, causing the flow to become chaotic and unpredictable.