Question

What is the significance of Bernoulli equation and Reynolds number in Fluid Mechanics?

Answer 1

• The Bernoulli equation is an relationship which relates pressure, velocity and height of a fluid flowing at one point along its flow.
• The Bernoulli equation says that for an ideal fluid, the sum of its potenital, kinetic and thermal energy must not change.
• This is very useful relationship between the 3 variables as it is applicable for many real-ilfe scenarios.
• The motion of airplanes when in flight and the flow of water from dams can be characterized using the bernoulli equation.
• As the equation is only applicable to ideal fluids, it also implies that energy losses due to the shear caused by viscosity and also non-laminar flow is responsible for major energy losses.
• Due to the simplicity and direct relationship between the variables, it is easy to calculate these variables at a point by designing another point in the flow whose variables can easily be calculated by the user.

• Reynolds number by definition is the ratio of inertial forces to viscous forces
• This ratio indicates whether a flow in a pipe with certain parameters ( velocity, diameter of pipe) of a fluid with parameters ( viscosity, density) is laminar or turbulent.
• The reynolds number is a crucial factor in determining the energy losses of the fluid as it flows through the pipe.
• Hydraulic operations are all based on pumping requirements and hence use the reynold's number.
• Reynold's number is also an indication on whether a given a flow is laminar or turbulent.
• Knowledge of laminar and turbulent flow is essential in designing effective heat and mass transfer operations