Mechanical Properties of Fluids Flashcards
Fluids
Substance that can flow
Characteristics of a fluid
- Atoms are arranged in a random manner
- Fluid cannot withstand tangential stress for an indefinite period
- Fluid has no definite shape of its own
- Can exert / withstand a force in a direction perpendicular to its surface
Fluid statics
Branch of physics that deals with the study of fluids at rest
Fluid dynamics
Branch of physics that deals with study of fluids in motion
Thrust
Total force exerted by a liquid on any surface in contact with it
Show that a liquid at rest exerts force perpendicular to surface of container at every point
- Suppose the liquid exerts a force F on the bottom surface in an inclined direction OA
- Tangential component: OC = Rcos theta
- Normal component: OD = Rsin theta
However, liquid is at rest, hence Rcos theta = 0; theta = 90 degree
Pressure
Thrust acting normally per unit area around that point
Fluid pressure
p = delta F / delta A
Density
Mass per unit volume
ro = M / V
Specific gravity
Ratio of density of substance to density of water at 4 degree celsius
Density formula (in terms of specific gravity)
Density = Specific gravity * Density of water at 4 degree Celsius
Pascal’s Law
- Pressure exerted at any point on an enclosed liquid is transmitted equally in all directions
- A change in pressure applied to an enclosed incompressible fluid is tranmitted undiminished to every point of the fluid and the walls of the containing vessel
- The pressure in a fluid at rest is same at all points if we ignore gravity
Derivation of Pascal’s Law
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Applications of Pascal’s Law
- Hydraulic Lift: Force multiplier; Small area force applied –> Larger area larger force
- Hydraulic Brakes: Piston attached to brake pedal through a lever system
Pressure exerted by a liquid column
W = Mass * g = Ah * ro * g
P = W / A = h * ro * g
Effect of Gravity on Fluid Pressure
derive
P2 - P1 = h * ro * g
* Liquid pressure is same at all points at the same horizontal level
* Pressure at any point depends upon h
* Absolute pressure P, at a depth h below the liquid surface open to atmosphere is greater than atmospheric pressure by amount h ro g
Gauge Pressure
Gauge pressure is the difference between the pressure being measured and the atmospheric pressure
Atmospheric Pressure
Pressure exerted by atmosphere
1.013 * 10^5 Nm^-2 or Pa or 1atm
Hydrostatic Paradox
Pressure exerted by a liquid column depends only on the height of the liquid column and not on the shape of the containing vessel
Mercury Barometer
- Measures atmospheric pressure
- 1m long glass tube closed at one end is filled with clean and dry mercury
- After closing the end of the tube with the thumb, the tube is inverted into a dish of mercury
Open - tube manometer
- U-tube containing some liquid
- One end of the tube is open to atmosphere and other end connected to vessel
- Total pressure P = pressure at A
Height of atmosphere
- Value of g does not change; temp remains uniform; assume density to be uniform
h ro g = pressure = 1.013 * 10^5 / 1.3 * 9.8 = around 8km
Systolic blood pressure is the top number and refers to the amount of pressure experienced by the arteries while the heart is beating.
Diastolic blood pressure is the bottom number and refers to the amount of pressure in the arteries while the heart is resting in between heartbeats.
Buoyancy
Upward force acting on a body immersed in a fluid is called upthrust / buoyancy
Centre of Buoyancy
Force of buoyancy acts through the centre of gravity of displaced fluid
Archemedes’ Principle
When a body is partially or wholly immersed in a fluid it experiences upward thrust equal to weight of fluid displaced by it and its upthrust acts through the centre of gravity of the displaced liquid
Streamline flow
When a liquid flows such that each particle of the liquid passing a given point moves along the same path and has the same velocity as its predecessor
Properties of streamlines
- No two streamlines can cross each other
- Tangent at any point on the streamline gives the direction of velocity of fluid particle
- Greater number of streamlines = Larger fluid velocty
- Fluid velocity remains constant at any point but may be different at different points of same streamline
Critical velocity
Critical velocity is the speed and direction at which a fluid flows through a conduit without becoming turbulent.
Tube of Flow
Bundle of streamlines forming a tubular region
Turbulent Flow
When liquid vel > critical vel = liquid flow becomes zig-zag