Control Volume Continuity Quiz: Test Fluid System Analysis

11th Grade

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| Questions: 20 | Updated: Mar 13, 2026

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1. The most general statement of continuity is:

Pressure is constant everywhere

Mass is conserved

Temperature is conserved

Speed is constant everywhere

Concept: general conservation law. Continuity is a mass balance. It can be written for a whole control volume or locally at a point.

Explanation

Concept: general conservation law. Continuity is a mass balance. It can be written for a whole control volume or locally at a point.

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About This Quiz

Control Volume Continuity Quiz: Test Fluid System Analysis - Quiz

This assessment focuses on the principles of control volume continuity in fluid system analysis. It evaluates understanding of mass conservation, flow rates, and the application of continuity equations. This knowledge is essential for engineers and scientists working with fluid mechanics, ensuring they can analyze and design efficient fluid systems effectively.

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2. A 'control volume' is an imaginary region used to apply conservation laws to flows.

True

False

Concept: control volume method. You track what enters and leaves the region. This approach works even when the flow is complex.

Explanation

Concept: control volume method. You track what enters and leaves the region. This approach works even when the flow is complex.

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3. The general control-volume mass balance can be summarized as:

Inflow + outflow = accumulation

Inflow − outflow = rate of change of mass inside

Outflow − inflow = 0 always

Pressure − speed = constant

Concept: mass balance sign convention. If more mass enters than leaves, mass inside increases. In steady flow, the rate of change term is zero.

Explanation

Concept: mass balance sign convention. If more mass enters than leaves, mass inside increases. In steady flow, the rate of change term is zero.

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4. For steady flow, the accumulation term is ______.

Concept: steady means no storage change. Steady flow implies properties at a fixed point do not change with time. Therefore mass inside a fixed control volume is not changing.

Explanation

Concept: steady means no storage change. Steady flow implies properties at a fixed point do not change with time. Therefore mass inside a fixed control volume is not changing.

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5. In vector form, incompressible flow is often written as:

∇×v = 0

∇·v = 0

∇p = 0 always

V = 0

Concept: divergence-free flow. ∇·v = 0 means no net 'source' or 'sink' of volume at a point. It is the local statement of incompressible continuity.

Explanation

Concept: divergence-free flow. ∇·v = 0 means no net 'source' or 'sink' of volume at a point. It is the local statement of incompressible continuity.

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6. ∇·v = 0 means fluid elements do not change volume as they move (incompressible).

True

False

Concept: local volume conservation. If the divergence is zero, flow into a tiny volume equals flow out. That matches the idea of no local expansion or compression.

Explanation

Concept: local volume conservation. If the divergence is zero, flow into a tiny volume equals flow out. That matches the idea of no local expansion or compression.

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7. For compressible flow, a common local continuity form is:

ρ = constant always

∂ρ/∂t + ∇·(ρv) = 0

∇·v = 1

∂p/∂t = 0

Concept: local compressible continuity. This equation tracks how density changes with time and how mass flows through space. It reduces to ∇·v = 0 when ρ is constant and steady.

Explanation

Concept: local compressible continuity. This equation tracks how density changes with time and how mass flows through space. It reduces to ∇·v = 0 when ρ is constant and steady.

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8. If density is constant and flow is steady, ∇·(ρv) = 0 reduces to ∇·v = 0.

True

False

Concept: reduction to incompressible form. With constant ρ, it factors out. Then the local condition becomes divergence-free velocity.

Explanation

Concept: reduction to incompressible form. With constant ρ, it factors out. Then the local condition becomes divergence-free velocity.

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9. The divergence ∇·v is best interpreted (at this level) as:

How fast the fluid heats up

How much the flow 'spreads out' or 'converges' at a point

The fluid’s colour intensity

The gravitational force

Concept: meaning of divergence. Positive divergence suggests local expansion (like a source), negative suggests convergence (like a sink). Zero means balance.

Explanation

Concept: meaning of divergence. Positive divergence suggests local expansion (like a source), negative suggests convergence (like a sink). Zero means balance.

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10. If more mass leaves a small region than enters, the density inside tends to ______ (if volume fixed).

Concept: link between flux and density. Outflow exceeding inflow removes mass from the region. With a fixed control volume, that lowers density (or mass) inside.

Explanation

Concept: link between flux and density. Outflow exceeding inflow removes mass from the region. With a fixed control volume, that lowers density (or mass) inside.

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11. Which statement best describes incompressible flow?

Pressure is zero

Density is approximately constant along the motion

Speed is constant everywhere

Viscosity is zero

Concept: definition. Incompressible means density changes are negligible. Speed can vary a lot even if the fluid is incompressible.

Explanation

Concept: definition. Incompressible means density changes are negligible. Speed can vary a lot even if the fluid is incompressible.

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12. A flow can be incompressible even if velocity changes from place to place.

True

False

Concept: incompressible ≠ constant speed. Incompressible only restricts density/volume changes. Continuity then forces the velocity field to adjust through divergence-free behavior.

Explanation

Concept: incompressible ≠ constant speed. Incompressible only restricts density/volume changes. Continuity then forces the velocity field to adjust through divergence-free behavior.

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13. In a 1D steady incompressible flow, continuity often appears as:

P + ½ρv² = constant

A(x) v(x) = constant

T(x) = constant

V(x) = constant

Concept: 1D continuity. This is the same q = av statement expressed along a varying area. It is a simplified form of mass conservation.

Explanation

Concept: 1D continuity. This is the same q = av statement expressed along a varying area. It is a simplified form of mass conservation.

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14. The control-volume form of continuity is useful even when the flow field is not uniform across an area.

True

False

Concept: integral form flexibility. The integral form sums mass flux over surfaces. You don’t need velocity to be uniform—only the total flux matters.

Explanation

Concept: integral form flexibility. The integral form sums mass flux over surfaces. You don’t need velocity to be uniform—only the total flux matters.

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15. Which statements are correct?

Continuity can be written in integral (control volume) form

Continuity can be written in differential (point) form

Incompressible flow often uses ∇·v = 0

Continuity requires pressure to be constant

Concept: forms of the same law. Continuity is mass conservation, not a pressure rule. Different mathematical forms apply to different problem setups.

Explanation

Concept: forms of the same law. Continuity is mass conservation, not a pressure rule. Different mathematical forms apply to different problem setups.

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16. If a velocity field has ∇·v > 0 at a point, a simple interpretation is:

Fluid is piling up there

The flow is locally expanding outward (source-like)

The fluid is freezing

Pressure must be zero

Concept: positive divergence. More 'flow out' than 'flow in' suggests expansion. For compressible flow, this can be linked to density decreasing.

Explanation

Concept: positive divergence. More 'flow out' than 'flow in' suggests expansion. For compressible flow, this can be linked to density decreasing.

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17. For water at modest speeds, treating the flow as incompressible is usually reasonable.

True

False

Concept: practical approximation. Water’s density changes very little with typical pressure variations. This makes incompressible continuity a good model in many applications.

Explanation

Concept: practical approximation. Water’s density changes very little with typical pressure variations. This makes incompressible continuity a good model in many applications.

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18. In many engineering problems, the point of using the differential form is to:

Avoid using conservation laws

Connect mass conservation to velocity and density fields locally

Eliminate units

Ignore geometry

Concept: local field description. Differential continuity describes how the flow behaves at each point. This is essential for deriving fluid equations and modeling complex flows.

Explanation

Concept: local field description. Differential continuity describes how the flow behaves at each point. This is essential for deriving fluid equations and modeling complex flows.

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19. Continuity still applies even if viscosity is large; viscosity affects energy losses, not mass conservation.

True

False

Concept: independence from viscosity. Viscosity changes how momentum and energy behave. Mass conservation remains true regardless of viscosity.

Explanation

Concept: independence from viscosity. Viscosity changes how momentum and energy behave. Mass conservation remains true regardless of viscosity.

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20. Which statement best captures why ∇·v = 0 is used for incompressible flow?

It makes the fluid stop moving

It expresses that there is no net local volume expansion or compression of the flow

It forces pressure to be constant

It only applies to gases

Concept: divergence-free condition. Incompressible flow conserves volume locally. Zero divergence is the mathematical way to express that balance at each point.

Explanation

Concept: divergence-free condition. Incompressible flow conserves volume locally. Zero divergence is the mathematical way to express that balance at each point.

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