Test: Reynolds model law - Civil Engineering (CE) MCQ

Reynold's number: 

• It is a dimensionless number that determines the nature of the flow of liquid through a pipe. 
• It is defined as the ratio of the inertial force to the viscous force for a flowing fluid.
• Reynold's number is written as Re.
• Re = Inertial force/Viscous force

Additional Information

• If  Reynold's number lies between 0 - 2000, then the flow of liquid is streamlined or laminar.
• If Reynold's number lies between 2000 - 3000, the flow of liquid is unstable and changing from streamline to turbulent flow. 
• If Reynold's number is above 3000, the flow of liquid is turbulent.

As submarine is completely submerged in water, thus Reynold’s number need to be same.
∴ (R_e)_model = (R_e)_prototype

V_m = 8 (16)
∴ V_m = 128 m/s
Point to remember:

• When body submerged ⇒ Reynold’s numbers are equal
• When body is floating ⇒ Froude’s numbers are equal.

Concept:
Water hammer is a phenomenon that is linked to the elasticity of the material and the only dimensionless parameter that involves elastic forces is Mach no.
Reynolds no. deals with viscous force, Froude no. with gravity and Weber no with surface tension.

Concept
For Dynamic similarity the ratio of corresponding forces acting at the corresponding points should be the same in the model and prototype, the ratio of these forces are called dimensionless numbers.
Therefore for the dynamic similarity between the model and prototype the dimensionless should also be the same. The models are designed on the basis of dominating forces.
Reynolds Model law is applicable for pipe flows and submarines airplanes, fully submerged bodies etc.
For dynamic similarity the Reynolds number must be the same.
Reynolds Number Re = VD/v
where V is the velocity, D is the pipe diameter,  ν is the kinematic viscosity
Calculation:
Given:
ν₁= 0.01 stoke, V₁ = 2 m/s, D₁ = D₂ = 15 cm, ν₂ = 0.03 stoke, 
Now  For dynamic similarity, Reynold’s number would be the same.

The relation between rpm (N), diameter (D) and head (H) is, 
Calculation:
Given: