State Newton's first law for a region of fluid.

The net velocity of a region of fluid remains constant unless acted on by a net force .

State Newton's second law for a region of fluid.

The net force acting on a region of fluid in a particular direction is equal to the rate of change of momentum of the region of fluid in that direction.

State Newton's third law for a fluid.

If an object applies a force on a fluid, the fluid applies an equal force in the opposite direction on the object.

How is a force at one end of a fluid in a tube transferred to the far end?

The fluid is incompressible , so each particle pushes its neighbors, transferring the macroscopic force through microscopic interactions between particles.

As a force is transferred through an incompressible fluid in a tube, the fluid's .......... remains constant.

As a force is transferred through an incompressible fluid in a tube, the fluid's density remains constant.

True or False? When a plunger pushes on the fluid in a syringe, only the fluid touching the plunger changes velocity.

False. The force is transferred through the fluid, so the fluid at the far end also changes momentum and accelerates out of the syringe.

Define buoyant force .

Buoyant force is the net upward force exerted on an object by the fluid it is in.

Why does a submerged cube experience a net upward force?

Its bottom surface is deeper, so it experiences a greater pressure and a greater perpendicular force than its top surface.

State Archimedes' principle .

The magnitude of the buoyant force is equal to the weight of the fluid displaced by the object.

What is true of the buoyant force on a floating object?

It is equal to the object's weight, because the submerged volume adjusts until the buoyant force balances the weight.

An object will .......... if its weight is greater than the maximum buoyant force.

An object will sink if its weight is greater than the maximum buoyant force.

True or False? Two fully submerged objects of identical shape but different masses experience the same buoyant force in the same fluid.

True. Buoyant force depends on the fluid's density and the volume displaced, not on the mass of the object.

Why does water flow out of a pipe at the base of a large tank?

The end of the pipe at the tank experiences a higher pressure because of the height of water above it (a large gauge pressure ), while the open end experiences only atmospheric pressure . This pressure difference drives the flow.

Why is there no flow if the pressure is equal at each end of a pipe?

There is no net force on the fluid, so it does not flow.

Why is the rate at which mass passes any point in a steady pipe flow constant?

The fluid is incompressible and flows steadily , so mass is conserved : the mass entering the pipe equals the mass leaving it in the same time.

Because density is constant, a constant mass flow rate means a constant .......... flow rate.

Because density is constant, a constant mass flow rate means a constant volume flow rate.

True or False? In steady flow, more mass passes the wide end of a pipe each second than the narrow end.

False. Mass is conserved, so the rate of flow of mass is the same at every point in the pipe, even where the width changes.

What happens to fluid speed when a pipe narrows ?

The fluid speed increases , because speed and cross-sectional area are inversely proportional .

The continuity equation is a consequence of the conservation of .......... and the incompressibility of the fluid.

The continuity equation is a consequence of the conservation of mass and the incompressibility of the fluid.

What are the three conditions for ideal fluid flow ?

The fluid is incompressible The fluid has no viscosity (no friction) The fluid moves smoothly through the pipe (no turbulence)

Which principle does Bernoulli's equation express?

Conservation of energy : with negligible viscosity no energy is dissipated, so the sum of the pressure, potential energy and kinetic energy terms is the same at both points.

Why must a reference height be chosen when using Bernoulli's equation?

Heights are only meaningful relative to a level, so an arbitrary reference height is needed to compare the heights of the two points.

Define streamline flow .

Streamline (or laminar ) flow is fluid moving smoothly through a tube along lines pointing in the direction of flow, without friction.

Define turbulent flow .

Turbulent flow is fluid flow in which the streamlines move in different directions and cross over , producing swirling vortices and unpredictable flow.

Fluids with slow flow speeds and low viscosity behave close to .......... flow.

Fluids with slow flow speeds and low viscosity behave close to streamline flow.

True or False? Bernoulli's equation accurately describes every real fluid flow.

False. It assumes ideal flow, so it is only a good approximation for some real-world scenarios, such as slow, low-viscosity flow.

What does Torricelli's theorem predict?

The speed of fluid leaving an opening in a container at a given depth below the fluid's surface.

What assumptions does Torricelli's theorem make?

The surface and the opening are both open to the same environment , so their pressures match The fluid speed at the surface is zero

From which equation is Torricelli's theorem derived?

Bernoulli's equation , applied between the fluid's surface and the opening.

The speed of fluid leaving an opening depends only on the .......... of the opening below the surface.

The speed of fluid leaving an opening depends only on the depth of the opening below the surface.

AP®PhysicsCollege BoardPhysics 1: Algebra-BasedFlashcardsUnit 8: FluidsFluid Mechanics

Fluid Mechanics (College Board AP® Physics 1: Algebra-Based): Flashcards

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State Newton's first law for a region of fluid.

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Cards in this collection (38)

State Newton's first law for a region of fluid.
The net velocity of a region of fluid remains constant unless acted on by a net force.
State Newton's second law for a region of fluid.
The net force acting on a region of fluid in a particular direction is equal to the rate of change of momentum of the region of fluid in that direction.
State Newton's third law for a fluid.
If an object applies a force on a fluid, the fluid applies an equal force in the opposite direction on the object.
How is a force at one end of a fluid in a tube transferred to the far end?
The fluid is incompressible, so each particle pushes its neighbors, transferring the macroscopic force through microscopic interactions between particles.
As a force is transferred through an incompressible fluid in a tube, the fluid's .......... remains constant.
As a force is transferred through an incompressible fluid in a tube, the fluid's density remains constant.
True or False?
When a plunger pushes on the fluid in a syringe, only the fluid touching the plunger changes velocity.
False.
The force is transferred through the fluid, so the fluid at the far end also changes momentum and accelerates out of the syringe.
Define buoyant force.
Buoyant force is the net upward force exerted on an object by the fluid it is in.
Why does a submerged cube experience a net upward force?
Its bottom surface is deeper, so it experiences a greater pressure and a greater perpendicular force than its top surface.
State Archimedes' principle.
The magnitude of the buoyant force is equal to the weight of the fluid displaced by the object.
State the equation for buoyant force.
$F_{b} = ρ V g$
- $F_{b}$ = buoyant force (N)
- $ρ$ = density of the fluid (kg/m³)
- $V$ = volume of fluid displaced (m³)
- $g$ = acceleration due to gravity (m/s²)
What does $V$ represent in the buoyant force equation for a partially submerged object?
The volume of the object below the surface, which equals the volume of fluid displaced.
What is true of the buoyant force on a floating object?
It is equal to the object's weight, because the submerged volume adjusts until the buoyant force balances the weight.
An object will .......... if its weight is greater than the maximum buoyant force.
An object will sink if its weight is greater than the maximum buoyant force.
True or False?
Two fully submerged objects of identical shape but different masses experience the same buoyant force in the same fluid.
True.
Buoyant force depends on the fluid's density and the volume displaced, not on the mass of the object.
Why does water flow out of a pipe at the base of a large tank?
The end of the pipe at the tank experiences a higher pressure because of the height of water above it (a large gauge pressure), while the open end experiences only atmospheric pressure. This pressure difference drives the flow.
Why is there no flow if the pressure is equal at each end of a pipe?
There is no net force on the fluid, so it does not flow.
Why is the rate at which mass passes any point in a steady pipe flow constant?
The fluid is incompressible and flows steadily, so mass is conserved: the mass entering the pipe equals the mass leaving it in the same time.
Because density is constant, a constant mass flow rate means a constant .......... flow rate.
Because density is constant, a constant mass flow rate means a constant volume flow rate.
State the equation for volume flow rate.
$\frac{V}{t} = A v$
- $V$ = volume of fluid passing a point (m³)
- $t$ = time taken (s)
- $A$ = cross-sectional area of the flow (m²)
- $v$ = speed of the flow (m/s)
True or False?
In steady flow, more mass passes the wide end of a pipe each second than the narrow end.
False.
Mass is conserved, so the rate of flow of mass is the same at every point in the pipe, even where the width changes.
State the continuity equation for two points in a pipe.
$A_{1} v_{1} = A_{2} v_{2}$
- $A_{1}$ = cross-sectional area at point 1 (m²)
- $v_{1}$ = flow speed at point 1 (m/s)
- $A_{2}$ = cross-sectional area at point 2 (m²)
- $v_{2}$ = flow speed at point 2 (m/s)
What happens to fluid speed when a pipe narrows?
The fluid speed increases, because speed and cross-sectional area are inversely proportional.
The continuity equation is a consequence of the conservation of .......... and the incompressibility of the fluid.
The continuity equation is a consequence of the conservation of mass and the incompressibility of the fluid.
True or False?
Fluid speeds up when a pipe widens, because the flow rate must stay constant.
False.
A wider pipe has a larger area, so the fluid slows down to keep the product $A v$ constant.
What are the three conditions for ideal fluid flow?
- The fluid is incompressible
- The fluid has no viscosity (no friction)
- The fluid moves smoothly through the pipe (no turbulence)
State Bernoulli's equation.
$P_{1} + ρ g y_{1} + \frac{1}{2} ρ v_{1}^{2} = P_{2} + ρ g y_{2} + \frac{1}{2} ρ v_{2}^{2}$
- $P$ = pressure at the point (Pa)
- $ρ$ = fluid density (kg/m³)
- $y$ = height of the point above the reference level (m)
- $v$ = fluid speed at the point (m/s)
Which principle does Bernoulli's equation express?
Conservation of energy: with negligible viscosity no energy is dissipated, so the sum of the pressure, potential energy and kinetic energy terms is the same at both points.
Why must a reference height be chosen when using Bernoulli's equation?
Heights are only meaningful relative to a level, so an arbitrary reference height is needed to compare the heights of the two points.
Define streamline flow.
Streamline (or laminar) flow is fluid moving smoothly through a tube along lines pointing in the direction of flow, without friction.
Define turbulent flow.
Turbulent flow is fluid flow in which the streamlines move in different directions and cross over, producing swirling vortices and unpredictable flow.
Fluids with slow flow speeds and low viscosity behave close to .......... flow.
Fluids with slow flow speeds and low viscosity behave close to streamline flow.
True or False?
Bernoulli's equation accurately describes every real fluid flow.
False.
It assumes ideal flow, so it is only a good approximation for some real-world scenarios, such as slow, low-viscosity flow.
What does Torricelli's theorem predict?
The speed of fluid leaving an opening in a container at a given depth below the fluid's surface.
State Torricelli's theorem as an equation.
$v = \sqrt{2 g ∆ y}$
- $v$ = speed of fluid leaving the opening (m/s)
- $g$ = acceleration due to gravity (m/s²)
- $∆ y$ = distance from the opening to the fluid's surface (m)
What assumptions does Torricelli's theorem make?
- The surface and the opening are both open to the same environment, so their pressures match
- The fluid speed at the surface is zero
From which equation is Torricelli's theorem derived?
Bernoulli's equation, applied between the fluid's surface and the opening.
The speed of fluid leaving an opening depends only on the .......... of the opening below the surface.
The speed of fluid leaving an opening depends only on the depth of the opening below the surface.
True or False?
The exit speed from an opening in a container depends on the fluid's density.
False.
The density cancels from both sides of Bernoulli's equation, so the exit speed depends only on $g$ and the depth.

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