8.3 Fluids and Newton’s Laws

Learning objectives

8.3A—Describe the conditions under which a fluid’s velocity changesDescribe the conditions under which a fluid’s velocity changes.• Newton’s laws can be used to describe the motion of particles within a fluid.• The macroscopic behavior of a fluid is a result of the internal interactions between the fluid’s constituent particles and external forces exerted on the fluid.8.3B—Describe the buoyant force exerted on an object interacting with a fluidDescribe the buoyant force exerted on an object interacting with a fluid.• The buoyant force is a net upward force exerted on an object by a fluid.• The buoyant force exerted on an object by a fluid is a result of the collective forces exerted on the object by the particles making up the fluid.• The magnitude of the buoyant force exerted on an object by a fluid is equivalent to the weight of the fluid displaced by the object. Relevant equation: TOPIC 8.3 Fluids and Newton’s Laws

Apply Newton’s second law

A fluid system changes its velocity when a net external force changes its momentum. For a constant-mass fluid parcel, a nonzero net force produces acceleration.

$\sum \vec F_{\text{external}}=\frac{d\vec p}{dt}=m\vec a$

Classify forces using the system boundary

Interaction	Role for the chosen fluid system
Collisions and forces between particles inside the fluid	Internal: transfer momentum between parts of the fluid
Gravity, a container wall, a piston, or another object acting on the fluid	External: can change the total momentum of the fluid system

Connect particles to fluid behavior

Microscopic particle interactions transmit forces through the fluid. Together with external forces, these interactions create the macroscopic patterns we observe, such as acceleration or changing flow speed.

Predict the velocity change

Example: model a $2.0\,\text{kg}$ parcel of fluid as having constant mass. If the net external force is $6.0\,\text{N}$ to the right,

$a=\dfrac{F_{\text{net}}}{m}=\dfrac{6.0}{2.0}=3.0\,\text{m s}^{-2}$ to the right.

Its velocity therefore changes by $3.0\,\text{m s}^{-1}$ each second while that net force acts.

Keep internal forces in their proper role

Internal forces do not vanish: they redistribute momentum within the fluid. But for the whole chosen system, internal force pairs cannot by themselves change total momentum; identify the system boundary before deciding which forces are external.

Combine distributed fluid forces

The buoyant force is the net upward force that a fluid exerts on an object. It is the combined result of forces from many fluid particles over the object’s surface.

Fluid pressure is greater on the deeper parts of the object than on the shallower parts. When all the distributed fluid forces are combined, their vertical components produce a net upward force.

Use the displaced-fluid weight

$F_B=\rho_{\text{fluid}}V_{\text{displaced}}g$

Quantity	Meaning	SI unit
$\rho_{\text{fluid}}$	Density of the fluid, not the object	$\text{kg m}^{-3}$
$V_{\text{displaced}}$	Volume of fluid displaced by the submerged part	$\text{m}^3$
$F_B$	Weight of that displaced fluid	N

Calculate the upward force

Example: an object displaces $0.020\,\text{m}^3$ of water with $\rho=1000\,\text{kg m}^{-3}$ . Using $g=9.8\,\text{N kg}^{-1}$ ,

$F_B=(1000)(0.020)(9.8)=196\,\text{N}$ upward.

This equals the weight of the displaced water.

Compare buoyancy with weight

Buoyant force is upward, but an object does not necessarily accelerate upward. Compare $F_B$ with the object’s weight: greater buoyant force gives upward acceleration, equal forces give zero vertical acceleration, and smaller buoyant force gives downward acceleration. Use only the displaced volume—not automatically the object’s full volume.

Next Topic

—8.4 Fluids and Conservation LawsRead