Exp 4 Reynolds Number 2014
MEHB221
Fluids Mechanics Lab
Experiment No. 4
REYNOLDS NUMBER
Objective
To investigate the relationship of flow condition and fluid velocity.
Apparatus
TecQuipment Reynolds Number and Transitional Flow Apparatus, H215 / 215A
TecQuipment Hydraulic Bench, H1
Figure 1: Schematic Diagram of Reynolds Number and Transitional Flow
Demonstration Apparatus
1
2014
MEHB221
Fluids Mechanics Lab
2014
Summary of Theory
Consider the case of a fluid moving along a fixed surface such as the wall of a pipe. At some distance ‘y’ from the surface the fluid has a velocity ‘u’ relative to the surface. The relative movement causes a shear stress ‘’ which tends to slow down the motion so that the velocity close to the wall is reduced below u. It can be shown that the shear stress produces a velocity gradient du / dy which is proportional to the applied stress. The constant of proportionality is the coefficient of viscosity and the equation is usually written as;
du dy …1
The above equation represents a model of a situation in which layers of fluid move smoothly over one another. This is termed “viscous” or “laminar” flow. The equation is valid and is a constant for a given fluid at a given temperature.
If the velocity is increased above certain value, small disturbances produce eddies in the flow which causes mixing between the high energy and low energy layers of fluid. This is called “turbulent flow” and under these conditions it is found that the relationship between shear stress and velocity gradient varies depending on many factors in addition to the viscosity of the fluid.
Reynolds realized that laminar flow is the result of viscous forces and that turbulent flow is in some way related to inertia forces. He postulated that the nature of flow depended on the ratio of inertia to viscous forces. This led to the derivation of a non-dimensional variable called Reynolds Number, Re.
Inertia forces are proportional to mass multiplied by velocity change divided by time.
Fluids Mechanics Lab
Experiment No. 4
REYNOLDS NUMBER
Objective
To investigate the relationship of flow condition and fluid velocity.
Apparatus
TecQuipment Reynolds Number and Transitional Flow Apparatus, H215 / 215A
TecQuipment Hydraulic Bench, H1
Figure 1: Schematic Diagram of Reynolds Number and Transitional Flow
Demonstration Apparatus
1
2014
MEHB221
Fluids Mechanics Lab
2014
Summary of Theory
Consider the case of a fluid moving along a fixed surface such as the wall of a pipe. At some distance ‘y’ from the surface the fluid has a velocity ‘u’ relative to the surface. The relative movement causes a shear stress ‘’ which tends to slow down the motion so that the velocity close to the wall is reduced below u. It can be shown that the shear stress produces a velocity gradient du / dy which is proportional to the applied stress. The constant of proportionality is the coefficient of viscosity and the equation is usually written as;
du dy …1
The above equation represents a model of a situation in which layers of fluid move smoothly over one another. This is termed “viscous” or “laminar” flow. The equation is valid and is a constant for a given fluid at a given temperature.
If the velocity is increased above certain value, small disturbances produce eddies in the flow which causes mixing between the high energy and low energy layers of fluid. This is called “turbulent flow” and under these conditions it is found that the relationship between shear stress and velocity gradient varies depending on many factors in addition to the viscosity of the fluid.
Reynolds realized that laminar flow is the result of viscous forces and that turbulent flow is in some way related to inertia forces. He postulated that the nature of flow depended on the ratio of inertia to viscous forces. This led to the derivation of a non-dimensional variable called Reynolds Number, Re.
Inertia forces are proportional to mass multiplied by velocity change divided by time.