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

In summary, the problem involves a horizontal bend in a pipeline with a discharge of 1000l/s and a gradual reduction in diameter from 600mm to 300mm. The flow is deflected at an angle of 60 degrees and the pressure at the larger end is 170000N/m^2. The task is to determine the magnitude and direction of the force exerted on the bend, specifically how to find pressure2 at the 300mm end. The attempted solution uses the moment equation to find the internal force, and then the pressure formula to find the pressure. The equation for flow discharge is Q=AV, and the external forces on the bend can be found using the Bernoulli equation.
  • #1
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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  • #2
Hint: Bernoulli equation
 

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

1. What is fluid mechanics?

Fluid mechanics is a branch of physics that studies the behavior of fluids (liquids and gases) at rest and in motion. It involves the study of the physical properties of fluids, such as density, viscosity, and pressure, as well as the forces and movements that act upon them.

2. What are some real-life applications of fluid mechanics?

Fluid mechanics has numerous real-life applications, including the design of airplanes and cars, the flow of blood in our bodies, the operation of pumps and turbines, and the behavior of ocean currents and weather systems. It is also used in industries such as oil and gas, aerospace, and environmental engineering.

3. How do you solve a fluid mechanics problem?

Solving a fluid mechanics problem involves applying the principles of fluid mechanics, such as conservation of mass, energy, and momentum, to a given scenario. This typically involves setting up equations and solving them using mathematical methods. It also involves making assumptions and simplifications to the problem to make it more manageable.

4. What is Bernoulli's equation and how is it used in fluid mechanics?

Bernoulli's equation is a fundamental equation in fluid mechanics that relates the pressure, velocity, and elevation of a fluid in a steady flow. It states that as the velocity of a fluid increases, the pressure decreases, and vice versa. This equation is used in various applications, such as calculating the lift force on an airplane wing and predicting the flow rate of a pipe.

5. What are the differences between laminar and turbulent flow?

Laminar flow is a type of fluid flow in which the particles of the fluid move in parallel layers, with very little mixing between layers. It is characterized by smooth and predictable flow patterns and is usually found in low-speed or highly viscous fluids. On the other hand, turbulent flow is a chaotic and unpredictable type of fluid flow, where the particles mix and swirl in a random manner. It is typically found in high-speed or low viscosity fluids and is responsible for phenomena such as eddies and turbulence.

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