Fluid Dynamics and Equations

What are the fundamental units used in fluid mechanics?

• Length (meter), Mass (kilogram), Time (second), Force (newton), Pressure (pascal), Density (kg/m³)

• Temperature (Celsius)

• Volume (liter)

• Velocity (meter/second)

Define Newtonian and non-Newtonian fluids with examples.

• Both Newtonian and non-Newtonian fluids have constant viscosity and behave the same under flow.

• Newtonian fluids are always gases, while non-Newtonian fluids are always solids.

• Newtonian fluids have variable viscosity and non-linear flow behavior, while Non-Newtonian fluids have constant viscosity and linear flow behavior.

• Newtonian fluids have a constant viscosity and linear flow behavior, while Non-Newtonian fluids have variable viscosity and non-linear flow behavior.

What characterizes laminar flow compared to turbulent flow?

• Laminar flow is always faster than turbulent flow.

• Laminar flow has smooth, parallel layers, while turbulent flow is chaotic and mixed.

• Turbulent flow has smooth, parallel layers like laminar flow.

• Laminar flow is characterized by random fluctuations and eddies.

State the continuity equation and explain its significance.

• The continuity equation is $ \nabla \cdot \mathbf{v} = 0 $ for incompressible flow.

• The continuity equation is expressed as \( \frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{v}) = 0 \), where \( \rho \) is the fluid density and \( \mathbf{v} \) is the velocity vector.

• The continuity equation states that mass can be created or destroyed in a fluid system.

• The continuity equation is only applicable to gases and not to liquids.

How does the Bernoulli equation relate pressure and velocity in a fluid?

• The Bernoulli equation indicates that pressure remains constant regardless of fluid velocity.

• The Bernoulli equation states that pressure and velocity are directly proportional.

• An increase in pressure leads to an increase in fluid velocity according to the Bernoulli equation.

• The Bernoulli equation shows that an increase in fluid velocity results in a decrease in pressure.

What assumptions are made in the Hagen-Poiseuille equation?

• The fluid is compressible and non-Newtonian.

• The assumptions made in the Hagen-Poiseuille equation include incompressible and Newtonian fluid, laminar flow, rigid cylindrical pipe, steady flow, and negligible friction losses.

• The pipe is flexible and can change shape.

• The flow is turbulent and varies with time.

Explain the concept of viscosity and its role in fluid flow.

• Viscosity determines the color of a fluid.

• Viscosity is the density of a fluid.

• Viscosity is a measure of a fluid's resistance to flow, affecting how easily it moves and its flow characteristics.

• Viscosity is the temperature of a fluid.

What is the difference between static and dynamic pressure in fluid systems?

• Dynamic pressure is the pressure of a fluid at rest.

• Static pressure is the pressure of a fluid at rest; dynamic pressure is the pressure due to fluid motion.

• Static pressure is caused by fluid motion.

• Static pressure is always higher than dynamic pressure.

How does temperature affect the viscosity of a fluid?

• Temperature inversely affects viscosity; higher temperatures decrease viscosity, while lower temperatures increase it.

• Viscosity increases with temperature and decreases with pressure.

• Higher temperatures increase viscosity while lower temperatures decrease it.

• Viscosity is unaffected by temperature changes.

Describe an application of the Bernoulli principle in real life.

• Water flowing through a pipe demonstrates the Bernoulli principle by reducing pressure.

• Car engines use the Bernoulli principle to increase fuel efficiency.

• A bicycle tire relies on the Bernoulli principle to maintain air pressure.

• Airplane wings utilize the Bernoulli principle to generate lift.