Fluid Mechanics – Part 2(9b)

What is steady flow in fluids?

• In steady flow, fluid properties at any specific point do not change with time.

• The values may vary from place to place, but remain constant at each location.

• Example: Water from a hose shows steady flow if the velocity at each point stays the same over time, even though the velocity differs between the supply pipe and the nozzle.

What is the difference between steady and unsteady flow?

• Steady flow: Conditions (like velocity) at any specific point do not change with time, even though they may vary from place to place.

• Unsteady flow: Conditions change with time, such as when a hose is first turned on and the flowrate increases.

What is one-dimensional flow?

• One-dimensional flow assumes all fluid properties are uniform across any cross-section and only vary along the direction of flow.

• In reality, this is rarely exact — e.g., in a pipe, velocity is zero at the wall and slower near the wall due to viscosity.

What does “representing fluid flows” mean?

• Fluid flows can be shown using lines that indicate the direction of motion.

• Several methods exist to represent flow patterns, each showing how the fluid moves in different ways.

What are streamlines?

• Streamlines show the direction of fluid flow at a given instant.

• They represent the direction of velocity of fluid particles throughout the flow field.

What are streamlines in fluid flow?

What are streaklines and streamlines?

• Streamlines: Show the instantaneous direction of fluid flow; no fluid crosses a streamline; in steady flow they don’t change with time.

• Streaklines: Connect all particles that passed through the same point over time (e.g., dye or smoke trails); in unsteady flow, they differ from streamlines.

What is the difference between streamlines and streaklines?

• Streamlines: Show the instantaneous direction of fluid flow; no particle crosses a streamline; in steady flow they stay fixed.

• Streaklines: Join particles that passed through the same point over time (e.g., dye/smoke). They differ from streamlines in unsteady flow.

What factors require a pressure difference in a moving fluid?

• Acceleration of the fluid (needs pressure difference to create force).

• Viscosity, which resists motion through shear stress.

• Mechanical (shaft) work done on or by the fluid (e.g., pumps or turbines).

What assumptions are made when using the Euler equation for fluid motion?

• Only elevation, density, and acceleration affect pressure.

• No viscosity (fluid is frictionless).

• No shaft work (no pumps or turbines adding/removing energy).

• Flow is steady and along a streamline.

What is the Bernoulli equation and where does it come from?

• The Bernoulli equation is obtained by integrating the Euler equation along a streamline.

• It relates pressure, velocity, and elevation in a flowing fluid, assuming steady, incompressible, non-viscous flow.

• Bernoulli’s equation comes from integrating the Euler equation along a streamline.

• It relates pressure, elevation, and velocity in steady, incompressible, frictionless flow.

What are viscous (real) fluids?

• Real fluids resist motion because of viscosity (internal friction).

• Higher viscosity = greater resistance to flow.

• Example: Oil is more viscous than water, so it flows more slowly.

What causes viscosity in real fluids?

• Liquids: Intermolecular forces create drag between layers moving at different speeds — like internal friction.

• Gases: Random molecular motion mixes fast and slow layers, transferring momentum and creating resistance.

What are laminar and turbulent flows?

• Laminar flow: Smooth, parallel pathlines; occurs at low velocities.

• Turbulent flow: Irregular, crossing pathlines; occurs at high velocities.

What is laminar flow?

• Occurs at low flowrates.

• Fluid particles move in smooth, parallel layers (laminae).

• No mixing across streamlines except minimal molecular diffusion.

Turbulent Flow (Short Version)

At high flowrates, fluid motion becomes chaotic. Particle paths are irregular, mixing is strong, and dye spreads quickly. Even if the overall flow is steady, local velocity fluctuates rapidly.

What is the transition region between laminar and turbulent flow?

• Between laminar and turbulent flow, a transition region exists where flow may switch between the two.

• At very low flowrates, flow is fully laminar across the pipe.

• At higher flowrates, flow becomes mostly turbulent, except for a thin laminar layer near the wall where turbulence cannot penetrate.

What causes viscosity in liquids and gases?

• Liquids: Intermolecular forces create drag between layers moving at different speeds — acts like internal friction.

• Gases: Molecules randomly move and mix between faster and slower layers, causing momentum transfer and resisting motion.

What is the Reynolds number and what does it represent?

• The Reynolds number (Re) is the ratio of inertial forces to viscous forces in a fluid.

• It is a dimensionless number (has no units).

• Re is used to predict flow regime:

  • Low Re → laminar flow

  • High Re → turbulent flow

How can fluid flow be classified?

• Steady vs Unsteady:

  • Steady: Properties at a point do not change with time (e.g., water flowing steadily from a hose).

  • Unsteady: Properties change with time (e.g., when a tap is first turned on).

• One-Dimensional Flow:

  • Assumes flow properties are uniform across a cross-section and vary only along the direction of flow.

  • Real flows are not perfectly 1-D because velocity is zero at the wall and slower near the walls due to viscosity.

What are the key flow types and governing equations in fluid mechanics?

• Flow types: Steady or unsteady; uniform or non-uniform; often approximated as one-dimensional.

• Euler & Bernoulli equations: Relate pressure, velocity, and elevation, describing energy and acceleration in ideal (non-viscous) flows.

• Real fluids: Have viscosity → can be laminar, turbulent, or transitional.

• Reynolds number (Re): Dimensionless ratio of inertial to viscous forces, determines flow regime.

How do streamlines, streaklines, and pathlines differ?

• Streamlines: Show instantaneous flow direction; no fluid crosses them.

• Streaklines: Show all particles that passed through the same point over time (e.g., dye/smoke).

• Pathlines: Show the actual path taken by a single particle.

• In steady flow, all three are identical.