Fluid Kinematics By : Me Edited from Mr. Basirul notes.

Fluid Kinematics

By : Me

Edited from Mr. Basirul notes

Continuity (Mass) EquationChapter 2 Lecture 2 2

Lagrangian Description

Introduced by Italian mathematician Joseph Louis Lagrange (1736–1813).

Treat a fluid particle such a snooker ball (keep track with particle)

Fluid in a container is treated as million, or maybe billions of fluid particle.

Microscopic point of view


Eularian Description

Introduced by Swiss mathematician Leonhard Euler (1707–1783)

Flow domain ( CONTROL VOLUME )

Define field variable in space of time within control volume (not keep track with the fluid particle movement), Pressure field, Velocity field, etc collectively Flow field

Experimental suit this method, (We see photos not fluid particles)

Macroscopic


Related terms in fluid motion

A streamline is a curve that is everywhere tangent to the instantaneous local Velocity vector.

A Pathline is the actual path traveled by an individual fluid particle over some time period.


Streamlines


Continuity equation

derived from Conservation of mass (What come in must come out)

Continuity (Mass) Equation


Definition of Mass Equation

Expression of mass conservation in the system

Learning motivation?Apply mass equation to balance flow rates of flow system


Mass Conservation

- Closed system = Mass remains unchanged

- Basic science; 16 kgs 02 + 2 kgs H2 18 kgs H20

- Mass conserved but can be converted to energy as E = mc2

- Means that mass changes when energy change

- Open System = Must keep track the entering and leaving masses


Control Volume Mass Equation

- Mass differential across CV is denoted as

- δ = dAc · ρ · Vn

- For the total flow rate, it can be written as;

m

c c

n c

A A

m m V dA

- Not a practical equation due to integral

- For simplification, we need Vavg instead of VnMass differential

(Cengel & Cimbala, 2006)


Control Volume Mass Equation (Contd.)

Average Velocity(Cengel & Cimbala, 2006)

- Actual and averaged velocity profile as shown

- For the average velocity can be written as;

1

c

avg n cc A

V V dAA

- For the flow with small density variation;

avg cm V A


Volume Flow Rate & Mass Conservation- Volume flow rate, can be written as;

c

n c avg c c

A

V V dA V A VA

- Mass flow rate and volume flow rate can be correlated as;

m V - For a CV, conservation of mass states;

CVin out

dmm m

dt


Volume Flow Rate & Mass Conservation (Contd.)

Arbitrary shape(Cengel & Cimbala, 2006)

- For arbitrary shape, rate of change of mass of CV;

CV

CV

dm ddV

dt dt

- Thus, total mass across CV can be written as;

net n

CS CS CS

m m V dA V n dA

- General mass conservation can be formulated as;

0CV CS

ddV V n dA

dt


Steady Mass Flow Conservation

Steady Flow Conservation

(Cengel & Cimbala, 2006)

- For steady flow across CV, mass is CONSTANT

- This means that;

in out

m m

- For incompressible flow, it is possible to write;

n n n nin out

V A V A


Examples & Tutorials

A garden hose attached with a nozzle is used to fill a 75L bucket. The inner diameter of the hose is 2.5cm and it reduces to 1.25cm at the nozzle exit. If the average velocity in the hose is 2.5 m/s. Determine the following properties;

(a) Volume and mass flow rates throughout the nozzle(b) How long it takes to fill in the bucket with water(c) Average velocity of water at the nozzle exit


Examples & Tutorials (Contd.)

Air enters a nozzle steadily at 2.21 kg/m3 and 30 m/s and leaves at 0.762 kg/m3 and 180 m/s. If the inlet area of the nozzle is 80 cm2, determine;

(a) Mass flow rate through the nozzle(b) Exit area of the nozzle



A hair dryer is basically a duct of constant diameter in which a few layers of electric resistors are placed. A small fan pulls the air in and forces it through the resistors where it is heated. If the density of air is 1.20 kg/m3 at the inlet and 1.05 kg/m3 at the exit, determine the percent increase in the velocity of air as it flows through the dryer;



A desktop computer is to be cooled by a fan whose flow rate is 0.34 m3/min. Determine the mass flow rate of air through the fan at an elevation of 3400 m where the air density is 0.7 kg/m3. Also, if the average velocity of air is not to exceed 110 m/min, determine the diameter of the casing of the fan



A smoking lounge is to accommodate 15 heavy smokers. The minimum fresh air for smoking lounges is specified to be 30 L/s per person (ASHRAE, Standard 62, 1989). Determine the minimum required flow rate of fresh air that needs to be supplied to the lounge, and the diameter of the duct if the air velocity is not to exceed 8 m/s



The minimum fresh air requirement of a residential building is specified to be 0.35 air change per hour (ASHRAE, Standard 62, 1989). That is, 35 percent of the entire air contained in a residence should be replaced by fresh outdoor air every hour. If the ventilation requirement of a 2.7 m-high, 200 m2 residence is to be met entirely by a fan, determine the flow velocity in L/min of the fan that needs to be installed. Also determine the diameter of the duct if the air velocity is not to exceed 6 m/s


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Energy Equation

Fluid Kinematics By : Me Edited from Mr. Basirul notes.

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