Momentum Transport

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Solving equations of change for the Boundary layer gives friction factor and drag

Examples

Flow through annular pipe

Flow between plates

Flow in planes

Flow through pipe

Momentum Transport

Macroscopic balance

Meachanical energy balance

Momentum balance

Mass balance

Macroscopic Variables

External flow

Drag

Internal flow

Friction

Microscopic Balance

Methods

Equations of Change

Shell balance

Important Concepts

Velocity gradients in a flow are confined to a thin layer near the wall. This layer is called Boundary layer. by solving equations of change for this layer skin frictional loss can be calculated

The three levels of study of TP are related to each other

Momentum Transport = Molecular Momentum Transport +  Convective Momentum Transport

Drag is the frictional force for external flow

Drag Coefficient

Skin friction loss is the frictional force exerted by fluid on the wall of a pipe (Ff-s). This is same as frictional loss calculated from Moody chart

Mechanisms

Convective Transport

Caused by Bulk flow by

Gravity

Pressure gradient

Molecular Transport

Pressure forces

viscous forces due to velocity gradients in flow

Tips for Test & Exam

Tip 10: Practice TP, Never study

Tip 9: For inclined planes and pipes, Learn to determine the component of gravity force acting on the flow

Tip 8: particle Re is Dp*V*rho / mu Dp is particle diameter, whereas rho and mu are fluid properties

Tip 7: Pressure in the macroscopic momentum balance equation should be gauge pressure

Tip 6: checking dimensional consistency of equations will help avoid errors

Tip 5 : If you are taking 40 minutes or less for the microscopic momentum balance problem, the remaining 80 minutes should be enough for the other 3 problems

Tip 4: if pressure not known, do not assume, Check if Bernoulli equation can be used to find it

Tip 3: Always assign r to the radial coordinate and z to the axial coordinate in cylindrical systems

Tip 2: when to use equations of change and when to use shell balance? The answer is: the choice is yours unless the question specifies the method. Given choice, I would prefer using equations of change. of course you need to justify when cancelling terms

Tip 1 : Please approach TP with an open mind. Get rid of all preconceived notions. Please talk to me to solve your problems / misunderstandings. The more you talk to me the more I can help