Chapter 9
Fluid Dynamics
Abstract Chapter 9 is concerned with fluid dynamics comprising equation of
continuity, Bernoulli’s equation, Torricelli’s theorem, Reynolds number, viscosity
and terminal velocity.
9.1 Basic Concepts and Formulae
Steady flow (laminar flow): In this type of flow, the velocity of the fluid (liquid or
gas) at a point is always the same although the velocity of the fluid may be different
at different points along the line of flow.
Irrotational flow: In this type of flow the element of fluid at each point has no net
angular velocity about that point. It implies the absence of eddies and vortices.
Incompressible fluid flow: A liquid is incompressible if its density is constant.
Stream lines are imaginary curves drawn through a fluid to indicate the direction
of motion of the flow of the fluid.
Tube of flow is a bundle of stream lines which define the boundary of the fluid.
Turbulent motion and Reynold’s number: For any liquid through a pipe there
exists a critical velocity at which the laminar flow suddenly changes into turbulent
type of flow. The stability of fluid flow is described by a dimensionless quantity
called Reynold’s number (R).
R = ρvd/η
(9.1)
where η and ρ are the viscosity and density of the fluid, respectively, d is the diameter of the pipe and v is the velocity. If
R < 2200, the flow is steady
R = 2200, the flow is unstable
R > 2200, the flow is usually turbulent
The Equation of Continuity
The principle of conservation of mass leads to the equation of continuity. For steady
flow, the mass of fluid passing all sections in a stream of fluid per unit time is
391
Fluid Dynamics
Abstract Chapter 9 is concerned with fluid dynamics comprising equation of
continuity, Bernoulli’s equation, Torricelli’s theorem, Reynolds number, viscosity
and terminal velocity.
9.1 Basic Concepts and Formulae
Steady flow (laminar flow): In this type of flow, the velocity of the fluid (liquid or
gas) at a point is always the same although the velocity of the fluid may be different
at different points along the line of flow.
Irrotational flow: In this type of flow the element of fluid at each point has no net
angular velocity about that point. It implies the absence of eddies and vortices.
Incompressible fluid flow: A liquid is incompressible if its density is constant.
Stream lines are imaginary curves drawn through a fluid to indicate the direction
of motion of the flow of the fluid.
Tube of flow is a bundle of stream lines which define the boundary of the fluid.
Turbulent motion and Reynold’s number: For any liquid through a pipe there
exists a critical velocity at which the laminar flow suddenly changes into turbulent
type of flow. The stability of fluid flow is described by a dimensionless quantity
called Reynold’s number (R).
R = ρvd/η
(9.1)
where η and ρ are the viscosity and density of the fluid, respectively, d is the diameter of the pipe and v is the velocity. If
R < 2200, the flow is steady
R = 2200, the flow is unstable
R > 2200, the flow is usually turbulent
The Equation of Continuity
The principle of conservation of mass leads to the equation of continuity. For steady
flow, the mass of fluid passing all sections in a stream of fluid per unit time is
391