Hydrodynamics Overview

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Questions and Answers

In turbulent flow, the motion of the fluid is irregular.

True

What is viscosity?

The degree of internal friction in a fluid.

Which of the following is NOT a property of an ideal fluid?

Steady motion

Incompressible

Turbulent motion (correct)

Non-viscous

The equation of continuity states that the product of the cross-sectional area of the pipe and the fluid speed at that cross-section is a ________.

constant Signup and view all the answers

Match the following properties with their definitions:

Viscosity = Internal friction between fluid layers Incompressible = Density remains constant Turbulent flow = Irregular and chaotic fluid motion Streamline flow = Smooth fluid motion without crossing paths Signup and view all the answers

What must be true about the mass of fluid in steady flow?

It must be conserved. Signup and view all the answers

What happens to liquid velocity when it moves through a constricted section of a pipe?

It increases Signup and view all the answers

What is the kinetic energy of a quantity of liquid with mass 'm' moving with velocity 'v'?

$\frac{1}{2} mv^2$ Signup and view all the answers

What type of fluid flow is characterized by smooth and parallel streamlines?

Laminar flow Signup and view all the answers

Which condition does NOT characterize an ideal fluid?

Compressible Signup and view all the answers

Streamlines can cross each other under steady-flow conditions.

False Signup and view all the answers

What is the term used for the degree of internal friction in a fluid?

Viscosity Signup and view all the answers

The velocity of liquid in turbulent flow is _____ and unsteady.

high Signup and view all the answers

What is the expression called that describes the principle that the product of the cross-sectional area and fluid speed at that section is constant?

Equation of continuity Signup and view all the answers

What is the formula for kinetic energy possessed by a quantity of liquid with mass 'm' moving with velocity 'v'?

$\frac{1}{2}mv^2$ Signup and view all the answers

In streamline flow, what happens to the volume of fluid flowing through different cross-sectional areas?

It remains constant Signup and view all the answers

What will happen to the fluid speed when the tube is constricted?

Fluid speed will increase Signup and view all the answers

Study Notes

Hydrodynamics

Fluid flow can be characterized as streamline (laminar) or turbulent.
Streamline flow: Each particle follows the same smooth path as previous particles.
Streamlines do not cross each other.
Streamline direction coincides with the fluid velocity at that point.
Turbulent flow: Irregular or chaotic flow, above a certain velocity or under conditions causing abrupt changes in velocity.
Eddy currents are characteristic of turbulent flow.
Viscosity: The degree of internal friction in a fluid.
Viscosity is the resistance between adjacent fluid layers moving relative to each other.
Fluids with lower viscosity flow more easily (e.g., kerosene).
Ideal fluid conditions:
- Non-viscous: No internal friction between adjacent layers.
- Incompressible: Constant density.
- Steady flow: Velocity, density, and pressure at any point do not change with time.
- No turbulence: No eddy currents.

Steady Flow of Liquids

Volume flow rate through different cross-sections of a pipe is constant if the fluid is incompressible.
A1v1 = A2v2
The volume of fluid entering one end of a tube equals the volume leaving in the same time interval (no leaks).
The equation is called the equation of continuity.

Kinetic Energy of a Liquid

A moving fluid possesses kinetic energy (1/2mv2).
Work done to move fluid to a pipe = difference of pressure × volume of fluid.
This work gives the fluid its kinetic energy.
Fluid velocity coming out of a tank is the same as if the fluid fell through the same height.
- v² = 2gh

Bernoulli's Equation

Relates pressure, speed, and elevation in a flowing fluid.
A consequence of energy conservation (ideal fluids).
The sum of pressure, kinetic energy per unit volume, and potential energy per unit volume is constant along a streamline.
- (1/2)pv² + pgh + p = constant
Assumes steady, incompressible, and inviscid flow.

Applications of Bernoulli's Equation

Vascular flutter: In arteriosclerosis, plaque constricts arteries, forcing higher blood speeds, potentially lowering pressure, and collapsing the artery.

Viscosity

Viscosity is the internal friction of a fluid, resisting the movement of one layer over another.
Non-viscous fluids: All fluid particles move at the same velocity through a pipe.
Viscous fluids: The fluid's velocity is maximum at the centre of the pipe and zero at the pipe walls; layers move at different velocities.

Flow of Fluids through Narrow Tubes

Laminar flow: Velocity profile depends on the radius of the tube.
- Velocity is greatest at the center and zero at the pipe wall.
Poiseuille's Law: Flow rate is inversely proportional to fluid viscosity but directly proportional to pressure difference and the fourth power of pipe radius.
- V = (π/8)(P₁ - P₂)(r⁴)/ηL

Motion Through a Viscous Medium (Stokes' Law)

Stokes' Law describes the resistive force on a sphere moving slowly in a viscous fluid.
The resistive force = 6πηrv.
Terminal velocity: Speed when the resistive force equals the weight and buoyant force.
Terminal velocity depends on size, density of the object and the surrounding fluid (viscosity and density).

Kinematic Viscosity

Ratio of dynamic viscosity to density.
V = µ/ρ

Reynolds Number

Indicates the flow type based on factors like fluid velocity, viscosity, density, and pipe radius.
Re = (ρVD)/µ.
Low Re: Laminar flow.
High Re: Turbulent flow.

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Description

Explore the principles of hydrodynamics, including the characteristics of streamline and turbulent flow. Learn about viscosity, ideal fluid conditions, and how these concepts influence the behavior of fluids in motion. Test your understanding of fluid dynamics concepts.