Bernoulli’s Equation - Hydraulics - Lecture Slides, Slides of Pneumatics

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• Bernoulli’s Equation

Review

Hydrostatic Forces on an Inclined, Submerged Surface

Buoyancy

Every submerged object has a buoyancy force and a weight force

Flow types

• Uniform Flow: Velocity does not change from point to point within the channel reach - Space criterion
• Steady Flow: Velocity does not change with respect to time - Time criterion
• Uniform flows are mostly steady

Turbulent and Laminar Flow

• Turbulent – mixed flow; random movement
• Laminar – smooth flow; fluid particles move in straight paths parallel to the flow direction
• Flow of water through a pipe is almost always turbulent

5 http://freshgasflow.com

Reynold’s # Example

• Given:
• Velocity=5 fps
• Diameter=1 foot
• Kinematic Viscosity @ 50F= 1.41E-5 (ft^2 /sec)
• Re=354,

Calculating Average Velocity

• V=Q/A

• Q=V*A

• Area must be perpendicular to flow

Continuity

• Q=A1V1=A2V

• If water flows from a smaller to larger pipe, then the velocity must decrease
• If water flows from a larger to smaller pipe, then the velocity must increase

Continuity Example

• A 120-cm pipe is in series with a 60-cm pipe. The rate of flow of water is 2 cubic meters/sec.
• What is the velocity of flow in each pipe?
• V 60 =Q/A 60 =7.1 m/s
• V 120 =Q/A 120 =1.8 m/s

Storage-Steady Flows

• Storage
• Qin=20 cfs
• Qout=15 cfs
• Storage rate=5 cfs
• If storage is in a tank what would you do to find the rate of rise?

Storage Example

• A river discharges into a reservoir at a rate of 400,000 cfs. The outflow rate through the dam is 250,000 cfs.
• If the reservoir surface area is 40 square miles, what is the rate of rise in the reservoir?

Break

Bernoulli’s Equation

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3 Forms of Energy

• Kinetic energy (velocity)
• Potential energy (gravity)
• Pressure Energy (pump/tank)

Kinetic Energy (velocity head)

• V^2 /2g
• Resulting units?