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

AI Thread Summary
The discussion revolves around calculating the pressure at the smaller end of a horizontal bend in a pipeline carrying water, where the flow transitions from a diameter of 600mm to 300mm and deflects at a 60-degree angle. The initial pressure at the larger end is given as 170,000 N/m², and the user seeks to determine the pressure at the smaller end and the force exerted on the bend. The approach involves using the continuity equation and Bernoulli's principle to relate pressures and velocities at both ends. The user has attempted to calculate internal forces and pressures using the formulas for flow discharge and pressure-area relationships. The urgency of the request indicates a need for prompt assistance in solving the problem.
alkhan22
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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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