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Lecture 3 Flashcards

(13 cards)

1
Q

How is the mass flow rate in and out of a system written WRT x-direction? How does this change for other directions?

A

dxdz for in, and dx)dydz changes for other directions

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2
Q

How do you calculate net mass flow rate for the x-direction? What is the equation for this in the continuity equation?

A

Net = out - in

Mass in element = rho * volume , where dxdydz is volume

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3
Q

What’s the equation for net mass flow rate out for all directions?

A

Sum of net flow for all directions

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4
Q

Rate of mass increase through system equation?

A
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5
Q

How do you get to the continuity equation?

A

Net flow out = Net mass decrease

RHS negative due to decreasing mass Divide both sides by dxdydz Set = 0
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6
Q

Tensor notation for continuity equation

A
First term = change in density (mass) Second term = net mass flow across fluid element
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7
Q

What is the divergence operator?

A
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8
Q

What does it mean if the divergence form of the continuity equation is greater than 0?

A

The system is expanding; if < 0, it’s contracting.

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9
Q

What is the divergence form of the continuity equation also known as?

A

Vector form

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10
Q

What is the LAGRANGIAN form of the continuity equation?

A
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11
Q

What does the total derivative expand into?

A
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12
Q

What are the definitions of substantial (total), local, and convective derivatives?

A

Total: rate of change of time following a moving fluid element

Local: rate of change of time at fixed point

Convective: rate of change of time due to movement of the fluid

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13
Q

What is the symbol for local and convective derivatives?

A

Local: ∂/∂t

Convective: u(∂/∂x)+v(∂/∂y)+w(∂/∂z)

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