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The Equation of Continuity

The equation of continuity expresses that for steady, incompressible fluid flow through a pipe with varying cross-sectional areas, the product of fluid velocity and cross-sectional area remains constant. It states that the mass flow rate entering a fluid system must equal the mass flow rate exiting the system. Mathematically, this can be represented as ρ1A1v1 = ρ2A2v2, where ρ is the fluid density, A is the cross-sectional area, and v is the fluid velocity. The equation is based on the principle of conservation of mass and describes fluid behavior in ideal flow situations.

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Yuke Djulianti
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351 views11 pages

The Equation of Continuity

The equation of continuity expresses that for steady, incompressible fluid flow through a pipe with varying cross-sectional areas, the product of fluid velocity and cross-sectional area remains constant. It states that the mass flow rate entering a fluid system must equal the mass flow rate exiting the system. Mathematically, this can be represented as ρ1A1v1 = ρ2A2v2, where ρ is the fluid density, A is the cross-sectional area, and v is the fluid velocity. The equation is based on the principle of conservation of mass and describes fluid behavior in ideal flow situations.

Uploaded by

Yuke Djulianti
Copyright
© Attribution Non-Commercial (BY-NC)
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PPTX, PDF, TXT or read online on Scribd
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THE EQUATION OF CONTINUITY

Presented By : Vika Tresnadiana Yuke Djulianti Yuli Nurul Maulida

DEFINITION

Definition of The Equation Continuity


The equation of continuty expresses that at ideal fluid flow, the cross product of fluid flow speed with its section area is constan.

THEORY AND FORM

If a fluid flows in a steady flow through a pipe with different section areas, then the volume of fluid that passes at each section is equally large in the same time interval. PIPA BERLUAS v1
PENAMPANG BESAR (A1) DENGAN LAJU ALIRAN FLUIDA (v1)

A1

A2 v2

v1

A1

Therefore the mass of iquid passing through part 1 during time interval t is :
m1 = 1 . V1 = 1 (A1 . x1) m1 = 1. A1 (v1. t)

PIPA BERLUAS PENAMPANG KECIL (A2) DENGAN LAJU ALIRAN FLUIDA (v2)

While the mass of fluid passing through part 2 during time interval t is :
m2 = 2 . V2 = 2 (A2 . x2) m2 = 2.A2(v2.t)

Because the fluid flow is steady, then the mass of fluid entering or passing through part 1 is equal to that of coming out or passing through part 2. So that obtained the following equation :
m1 = m2 1.A1.v1.t = 2.A2.v2.t

Because the multiplication between speed of fluid flow and section area (A.v) is known as debit (Q), then the equation of continuity in ideal fluid can also be expresses as flows :
Q1 = Q2 Q1 = k

DEBIT

If a fluid flows in a pipe with section area A and the velocity of fluid v, then the amount of flluid (volume) that flows passing that section per unit of time is called debit. In the form of equation,V/t Q = debit is formulated as follow :

Where : Q = debit of fluid flow (m3/s) V = volume of fluid in motion (m3) t= time (s)

Because the volume of fluid V = section area A x length of part l Q = A l /t Because the length of part l divided by time t is the velocity of fluid flow, then the equation above can be written as follows A v Q=:

Where : A = section area (m3) v = the velocity of fluid flow (m/s)

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