Fluid Dynamics: Continuity and Bernoulli's Principle

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Questions and Answers

Which statement accurately reflects the implications of Bernoulli's Equation?

It indicates that pressure increases with both velocity and height.

It applies to both ideal and real fluids without any restrictions.

It suggests that the kinetic energy term dominates pressure energy at high velocities.

It holds true only in inviscid flow and along a streamline. (correct)

In the context of fluid dynamics, how does pressure change in a viscous fluid flowing through a pipe?

Pressure fluctuates erratically with no predictable pattern.

Pressure decreases along the length of the pipe due to energy dissipation. (correct)

Pressure remains constant regardless of fluid velocity.

Pressure increases significantly at points of constriction.

Identify the correct expression correlating work done and changes in energy for a fluid system.

Work done equals the difference in potential energy alone.

Work done is independent of changes in fluid density.

Work done is equal to the change in kinetic energy plus pressure energy.

Work done balances with the total change in kinetic and potential energy. (correct)

What is the significance of the term $\frac{1}{2}\rho v^2$ in fluid mechanics?

It indicates the bulk motion kinetic energy of the fluid. Signup and view all the answers

Which of the following points is NOT a characteristic of an ideal fluid as described in the content?

An ideal fluid experiences pressure decreases along a streamline. Signup and view all the answers

What does Bernoulli's Principle state about the relationship between pressure and velocity in a flowing fluid?

As velocity increases, pressure decreases. Signup and view all the answers

Which of the following accurately describes the continuity equation?

The mass flow rate of a fluid remains constant throughout a streamline. Signup and view all the answers

Considering flow dynamics, what is the effect of increasing viscosity on fluid flow?

It consistently decreases the flow rate. Signup and view all the answers

Which characteristics define an ideal fluid?

It is constant in density, nonviscous, and steady in flow. Signup and view all the answers

How is pressure in a fluid defined in terms of its depth?

Pressure increases with depth due to weight of the fluid above. Signup and view all the answers

What does the Reynolds number indicate about fluid flow?

It determines the flow characteristics as laminar or turbulent. Signup and view all the answers

In the context of energy conservation in fluids, which of the following principles is most relevant?

Total mechanical energy of an ideal fluid remains constant along a streamline. Signup and view all the answers

What happens to the flow of a fluid when it transitions from a laminar to a turbulent state?

The flow becomes less predictable and chaotic. Signup and view all the answers

How does Bernoulli's principle explain the roof loss during a storm?

Pressure difference occurs due to faster flow above the roof. Signup and view all the answers

What does the Continuity Equation state about fluid flow in a pipe?

Higher velocity results in lower pressure, maintaining mass flow rate. Signup and view all the answers

In what way does the Venturi effect relate to fluid pressure and velocity?

Narrowing a flow tube causes the fluid to speed up while pressure drops. Signup and view all the answers

What is the underlying reason rabbits do not suffocate in their burrows?

Burrows must have multiple openings to ensure air circulation. Signup and view all the answers

Which phenomenon explains why a baseball curves in flight?

Asymmetrical flow patterns create a pressure difference. Signup and view all the answers

What role does energy conservation play in fluid dynamics according to Bernoulli’s principle?

Total mechanical energy of the fluid remains constant throughout flow. Signup and view all the answers

What happens to ship pressure while passing closely to each other?

They create larger pressure differences, causing suction. Signup and view all the answers

What is the consequence of airflow disturbed by a house during a storm?

Pressure above the roof drops due to faster airflow, potentially lifting it. Signup and view all the answers

Study Notes

Fluid Dynamics - Equation of Continuity and Bernoulli's Principle

Fluid Dynamics: Study of fluids in motion
Fluid Statics: Study of fluids at rest
Reynolds Number (Re): Dimensionless quantity characterizing fluid flow. Determines if flow is laminar or turbulent.
- Formula: Re = ρνL/η
- ρ = density of fluid
- ν = average flow velocity
- L = characteristic dimension (e.g., diameter of pipe)
- η = viscosity
Laminar Flow: Smooth, orderly flow. Re < ~2000
Turbulent Flow: Chaotic, irregular flow. Re > ~2000
Ideal Fluid: Hypothetical fluid possessing:
- Incompressible: Constant density
- Irrotational: Smooth flow, no turbulence
- Nonviscous: No internal friction
- Steady Flow: Velocity at each point is constant over time
Streamlines: Lines indicating the direction of fluid flow at a specific moment.
- Streamlines cannot cross
Equation of Continuity: Conservation of mass in a fluid flow.
- A₁V₁ = A₂V₂ (where A is cross-sectional area and V is velocity at sections 1 and 2 of a flow tube)
Bernoulli's Principle: In ideal fluid flow, increased fluid speed results in decreased pressure.
- P₁ + 1/2ρv₁² + ρgy₁ = P₂ + 1/2ρv₂² + ρgy₂ (where P is pressure, ρ is density, v is velocity, g is acceleration due to gravity, and y is height)
Venturi Effect: A constriction in a flow tube causes increased velocity and decreased pressure, leading to different pressures within the tube relative to surrounding pressure.

Applications of Bernoulli's Principle and Continuity

Rivers: Velocity changes with changes in river width
Circulatory Systems: Blood flow is governed by pressure differences
Respiratory Systems: Inhalation and exhalation due to air pressure changes
Air conditioning systems: Air flow is related to changes in pressure and volume
Aircraft flight: Pressure difference between upper and lower surfaces of wings creates lift
Spray guns: Compressed air accelerates paint for application
Blood Flow: Velocity and cross-sectional area of blood vessels affect total blood flow rate
House roof in a storm: Air speed over the house top increases due to wind resulting in lower pressure and causing roofs to be lifted off
Burrows: Air movement through separate burrow entrances creates a pressure differential which maintains airflow

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Description

Explore the fundamental concepts of Fluid Dynamics, including the equation of continuity and Bernoulli's principle. This quiz covers key topics such as laminar and turbulent flow, Reynolds number, and the characteristics of ideal fluids. Test your understanding of how fluids behave in motion and at rest.