MECHANICS OF FLUIDS

FLUIDS

Anything that can flowLiquid and Gases

Fluid DynamicsFluid Static- Study of fluids in motion

- study of fluids at rest

Density- ratio of mass of a substance to its volume

V

m

= densitym = massV = volume

Unit: kg/m3

Density

When the can is squeezed, the density increases.

What will happen to its density?

Density

Pressure- force per unit area

A

FP

P = pressureF = forceA = area

Unit: N/m2 or Pa

Pressure

Pressure

PressureIt is the same any particular depth in liquid contained in vessels of different sizes or shape.

12 Pa

12 Pa

12 Pa

1. Pascal’s Principle

The pressure applied at any given point on a confined fluid is transmitted undiminished throughout the fluid.

Application

1. Pascal’s Principle

The pressure applied at any given point on a confined fluid is transmitted undiminished throughout the fluid.

Application

This is much better!

1. Pascal’s Principle

The pressure applied at any given point on a confined fluid is transmitted undiminished throughout the fluid.

2

2

1

1

21

A

F

A

F

PP

1. Pascal’s Principle

F1 = 2500 N F2 = ? W = 10000 NA1 = 2 m2 A2 = 8 m2

2

2

1

1

21

A

F

A

F

PP

2. Bernoulli’s Principle

- As the velocity of the fluid increases, its pressure decreases

BuoyancyThe fluid always go from high pressure area to low pressure

area

What will happen if the train passes on your side?

Lower velocityHigher pressure

Higher velocityLower pressure

Buoyancy

- upward force when object is submerge in fluid

Buoyant force

3. Archimedes’ Principle

A body partly or entire submerged in a fluid is buoyed up by a force equal in magnitude to the weight of the displaced fluid.

BF = Wair - Wwater

BF = Wfluid displaced

Problems1. An 80 kg metal cylinder 2m long and with each end of area 25 cm2 stands vertically on one end. What pressure does the cylinder exert on the floor?

2. A piston of cross-sectional area "a" is used in a hydraulic press to exert a small force of magnitude "f" on the enclosed liquid. A connecting pipe leads to a larger piston of cross-sectional area A. If the piston diameters are 3.80 cm and 53.0 cm, what force magnitude on the small piston will balance a 20.0 kN force on the large piston?

Problems

3. What is the maximum weight a solid, square, pinewood raft measuring 4.0 m on a side and 0.30 m thick support and still float in water? How much weight can we add in the raft so that it can still float? wood = 420 kg/m3

4. A solid aluminum cylinder, = 2700 kg/m3 weighs 0.067 kg in air and 0.045 kg in turpentine. Determine the density of the turpentine.