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Continuity equation..pptx
Continuity equation.
Learning objectives
to apply continuity equation to solve problems
Schedule of lesson:
- Derivation of equation of continuity
- Solving problems for continuity equation
Consider a tube with a varying cross sectional at both ends.
Show liquid flow
Volume in
Volume out
The amount of water coming in must be equal to the amount of water coming out per time.
The flow rate of liquid, Q1 and Q2, at both points must be equal.
1
2
𝑄 1 𝑄𝑄 𝑄 1 1 𝑄 1 = 𝑄 2 𝑄𝑄 𝑄 2 2 𝑄 2
Flow rate is the amount of water per time.
𝑸= 𝑽 𝒕
1
2
𝑄 1 𝑄𝑄 𝑄 1 1 𝑄 1 = 𝑄 2 𝑄𝑄 𝑄 2 2 𝑄 2
𝐴 1 𝐴𝐴 𝐴 1 1 𝐴 1
𝐴 2 𝐴𝐴 𝐴 2 2 𝐴 2
𝐿 1 𝐿𝐿 𝐿 1 1 𝐿 1
𝐿 2 𝐿𝐿 𝐿 2 2 𝐿 2
𝑣 1 𝑣𝑣 𝑣 1 1 𝑣 1
𝑣 2 𝑣𝑣 𝑣 2 2 𝑣 2
𝑉 1 𝑡 = 𝑉 2 𝑡
What is the relationship between cross sectional area and the velocity?
𝑉=𝐴𝐿
𝐴 1 𝐿 1 𝑡 = 𝐴 2 𝐿 2 𝑡
𝑣= 𝐿 𝑡
𝑨 𝟏 𝒗 𝟏 = 𝑨 𝟐 𝒗 𝟐
𝑨𝒗=𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕
Solve problems
THANK YOU!
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