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Fluid Mechanics: Unsteady Flow in Pipelines

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Fluid Mechanics: Unsteady Flow in Pipelines

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Questions and Answers

What does the continuity equation imply for incompressible fluid flow in a pipeline?

The temperature of the fluid is the primary variable affecting flow.

The pressure can change freely without affecting the mass flow rate.

The velocity of the fluid must increase with decreasing cross-sectional area.

The mass flow rate must remain constant along the pipeline. (correct)

In the context of the continuity equation, what do the symbols rac{ ext{A}}{ ext{t}} and rac{ ext{Q}}{ ext{x}} represent?

Change in area with respect to time and change in pressure with respect to distance.

Cross-sectional area at a given moment and total flow rate in the pipe.

Instantaneous area and total pressure drop along the pipeline.

Change in cross-sectional area over time and change in mass flow rate along the pipe. (correct)

Which equation is used alongside the continuity equation to describe unsteady flow in a pipeline for incompressible fluid?

Momentum equation. (correct)

Energy equation.

Navier-Stokes equations.

Bernoulli's equation.

According to the continuity equation for incompressible fluid flow, if the cross-sectional area of the pipe decreases, what happens to the mass flow rate?

<p>It remains constant.</p> Signup and view all the answers

What would be a consequence of failing to satisfy the continuity equation in a pipeline with incompressible fluid flow?

<p>Pressure losses will occur due to varying mass flow rates.</p> Signup and view all the answers

Study Notes

Unsteady Flow in a Pipeline

The flow of an incompressible fluid in a pipeline can be described using the continuity and momentum equations.
The continuity equation states that the mass flow rate must remain constant for an incompressible fluid which means that the rate at which fluid enters a section of the pipe must be equal to the rate at which it leaves.
The continuity equation for this flow is:
( \frac{\partial A}{\partial t} + \frac{\partial Q}{\partial x} = 0 ) where:
( A ) = cross-sectional area of the pipe.
( Q ) = volumetric flow rate.
This equation implies that any change in the cross-sectional area of the pipe must be accompanied by a corresponding change in the flow rate.

Momentum Equation

The momentum equation describes the forces acting on the fluid due to pressure gradients, friction, and gravity. This equation can be used to predict the flow velocity and pressure distribution within the pipe.

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Description

This quiz focuses on the principles of unsteady fluid flow in pipelines, highlighting the continuity and momentum equations. Understand how mass flow rates and pressure gradients affect fluid dynamics within pipe systems. Test your knowledge on the mathematical representations and their implications for real-world applications.