Stream-lined and Turbulent Flow | Equation of Continuity | Physics Grade 11 Notes

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Stream-lined and Turbulent Flow | Equation of Continuity | Physics Grade 11 Notes

Stream-lined and Turbulent Flow | Equation of Continuity

Stream-lined and Turbulent Flow

Stream-lined Flow: When the flow of liquid is such that the velocity, v of every particle at any point of the fluid is constant, then the flow is said to be steady or streamline flow.

Turbulent flow: If the liquid is flowing with an unequal velocity greater than its critical velocity then the flow of liquid is called turbulent flow.

Equation of continuity
Let us consider streamline flow of a non-viscous and incompressible liquid through a non-uniform tube as shown in the figure, Let A1, v1, and A2, v2 are the area and velocities of liquid at section x and y respectively.

Equation of ContinuityNow, mass per second of liquid entering the tube through section X = A1 v1ϱ1 and mass per second of liquid leaving the tube through section Y = A2 v2ϱ2

If the liquid doesn’t overflow, then m1 = m2, or A1 v1ϱ1 = A2 v2ϱ2
 
Since the density of the liquid is same in both sections
A1v1 = A2v2
This equation of continuity i.e. volume per second of liquid entering the tube is equal to the volume per second of liquid leaving from another section.
 
The energy possessed by liquid;
1. Kinetic Energy: The energy possessed by liquid by the virtue of its motion. Let a liquid of mass ‘m’ is moving with velocity ‘v’ then its K.E. is given by
K.E. = ½ mv2
K.E. per unit mass of liquid = ½ v2
K.E. per unit volume of liquid = ½ ϱ v2
 
2. Potential Energy: Energy possessed by liquid by virtue of its position is called Potential Energy of liquid. Let a liquid of mass ‘m’ is kept height ‘h’ above from the ground surface, then its Potential Energy is given by
P.E. = mgh
P.E. per unit mass = gh
P.E. per unit volume = ϱgh
 
3. Pressure Energy: Energy possessed by liquid by virtue of pressure force is Pressure Energy. The pressure of the liquid is given by,
Pressure Energy= PA x
Pressure Energy = PV
Where P is pressure and V is volume of liquid & x is the distance moved.
Pressure energy per unit mass = P/ϱ
Pressure energy per unit volume = P

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