For no turbulency, Reynolds number must be critical.

Fluid Flow and Tube Diameter:
The given problem involves the flow of a fluid through a tube of a certain diameter. The diameter of the tube is provided as 20 cm, which can be converted to meters by dividing it by 100. Therefore, the tube diameter is 0.2 meters.

Fluid Density and Viscosity:
The fluid in question has a density of 100 kg/m3 and a viscosity of 0.5 N-s/m2. Density is a measure of the mass per unit volume of the fluid, while viscosity is a measure of the fluid's resistance to flow.

Flow Regime:
The problem specifies that there is no turbulency in the flow, which suggests that the flow regime is laminar. In laminar flow, the fluid flows smoothly in parallel layers without any mixing or turbulence.

Velocity Distribution in Laminar Flow:
In laminar flow, the velocity distribution across the tube follows a parabolic profile. The maximum velocity occurs at the center of the tube, while the velocity decreases towards the walls of the tube. This velocity profile is known as Hagen-Poiseuille flow.

Hagen-Poiseuille Equation:
The Hagen-Poiseuille equation relates the flow rate, tube diameter, fluid viscosity, and pressure drop across the tube. For laminar flow in a circular tube, the equation is given as:

Q = (π * r^4 * ΔP) / (8 * μ * L)

where Q is the volumetric flow rate, r is the tube radius, ΔP is the pressure drop across the tube, μ is the fluid viscosity, and L is the length of the tube.

Calculating Maximum Velocity:
To calculate the maximum velocity, we need to determine the volumetric flow rate. Since the problem does not provide information about the pressure drop or the length of the tube, we can assume that the pressure drop and tube length are such that they do not affect the maximum velocity.

Therefore, we can rearrange the Hagen-Poiseuille equation to solve for the maximum velocity (Vmax):

Vmax = (Q / A)

where A is the cross-sectional area of the tube.

Calculating Cross-sectional Area:
The cross-sectional area of the tube can be calculated using the formula for the area of a circle:

A = π * r^2

where r is the tube radius.

Substituting Values:
Substituting the given values into the equations:

r = 0.2 / 2 = 0.1 m

A = π * (0.1)^2 = 0.0314 m2

Calculating Maximum Velocity:
Finally, substituting the calculated values into the equation for maximum velocity:

Vmax = (Q / A) = (Q / 0.0314)

Since we don't have information about the flow rate (Q), we cannot calculate the exact maximum velocity. However, the correct answer is given as 50 (rounded to the nearest integer), which suggests that the flow rate is such that the maximum velocity is 50 m/s.