Fluid Mechanics: Pressure Calculation for a Horizontal Bend in a Pipeline

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SUMMARY

The discussion centers on calculating the pressure at the smaller end of a horizontal bend in a pipeline conveying water at a discharge rate of 1000 l/s, with a diameter reduction from 600 mm to 300 mm and a deflection angle of 60 degrees. The pressure at the larger end is given as 170,000 N/m². The user employs the formula F = P/A to determine the internal force and utilizes the continuity equation Q = A * V to relate flow discharge to velocity. The Bernoulli equation is suggested for further analysis of external forces acting on the bend.

PREREQUISITES
  • Understanding of fluid dynamics principles, specifically Bernoulli's equation.
  • Knowledge of flow continuity and the continuity equation Q = A * V.
  • Familiarity with pressure calculations in fluid mechanics.
  • Basic skills in applying force equations in fluid systems.
NEXT STEPS
  • Study the application of Bernoulli's equation in pipeline flow scenarios.
  • Learn about the effects of pipe diameter changes on flow velocity and pressure.
  • Research methods for calculating forces on bends and fittings in fluid systems.
  • Explore advanced fluid mechanics topics such as turbulent vs. laminar flow and their effects on pressure loss.
USEFUL FOR

Students and professionals in engineering, particularly those specializing in fluid mechanics, pipeline design, and hydraulic systems, will benefit from this discussion.

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Homework Statement



A horizontal bend in a pipeline conveys water at a discharge at 1000l/s gradually reduces from 600mm to 300mm and deflects the flow through an angle of 60 degrees. At the larger end the pressure is 170000N/m^2. Determine the magnitude and direction of the force exerted on the bend.




Homework Equations


How can I find pressure2 (at point 2 300mm end)

is my solution right to find pressure at point 2

Please help as i need solution urgently. Thanks to all

The Attempt at a Solution



I have used moment to find internal force F=DENSITY * FLOW DISCHARGE (V2-V1)

Than I have used the formula F=P/A to find the pressure.

Q(FLOW DISCHARGE) =AV (AREA*VELOCITY)

P.s if i find p2 i can use formula to find external forces on the bend using

P1A1-P2A2COSTHETA -Fx= DENSITY*Q*(V2*COSTHETA-V1)

Fy-P2A2SINTHETA= DENSITY*Q*(V2*SINTHETA)
 
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Hint: Bernoulli equation
 

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