321ATTENTION!!!!!!

Continuity Equation

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Suhartini Lestari PutriWida Maya Mustika

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Definition Formula

Application Conclusion

Continuity Equation

• Continuity equation is the flow rate has the same value (fluid isn’t appearing or disappearing) at every position along a tube that has a single entry and a single exit for fluid flow.

• This principle is known as the conservation of mass.

• This equation for the ideal fluid (incompressible, nonviscous and has steady flow).

Definition

m1 = m2

ρ1.V1 = ρ2.V2

ρ1 (A1.x1) = ρ2 (A2.x2)

ρ1.A1 (v1.Δt1) = ρ2.A2 (v2.Δt2)

Formula

Formula :

A1 v1 = A2 v2

Where :A = Area (m2)v = Velocity (m/s)

Formula

Q= Av = V/tWhere :Q = rate (m3/s)A = Area (m2)v = Velocity (m/s)V = Volume (m3)t = time (s)

Formula

Application in daily life

The velocity water of garden hose before we hold it and after we hold it

The river with different area which change along their length

Water gunVolumetric pipetteEtc..

A2

A1

V1

V2

Example of Continuity Equation in The River

Area

Area

Area

Problem Sample

Fluid flows in the pipe that has differrent radius, radius and velocity of position A are 3 cm and 8m/s, how much the velocity of water of position B and C, if radius of B and C are 1 cm and 5 cm? Known : rA= 3cm → 3 x 10-2 m2 vA= 8m/s

rB= 1 cm → 1 x 10-2 m2 rC= 5 cm → 5x 10-2 m2

Question : vB and vC?Answer :

Conclusion

• Continuity Equation says fluid speeds up going to smaller opening, slows down going to larger opening

• Velocity of fluid which is incompresible Inverse with area of the pipe where the fluids are flowing

Sources

• EBVF4103 (Chapter 3) Fluid Mechanics for Civil Engineering

• http://ctmd.oum.edu.my/v2/tutorkits/

The End