Continuity Equation Quiz: Test Conservation In Fluid Flow

9th Grade

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| Questions: 20 | Updated: Mar 13, 2026

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1. For steady incompressible flow, the continuity equation is often written as:

A + v = constant

A₁v₁ = a₂v₂

Pv = constant

ρ + a = constant

Concept: continuity equation. If density is constant and flow is steady, the volume flow rate is constant along the pipe. That means area times speed stays the same.

Explanation

Concept: continuity equation. If density is constant and flow is steady, the volume flow rate is constant along the pipe. That means area times speed stays the same.

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About This Quiz

Continuity Equation Quiz: Test Conservation In Fluid Flow - Quiz

This assessment focuses on the principles of continuity and flow rate in fluid dynamics. It evaluates your understanding of key concepts such as the conservation of mass and the relationship between velocity and cross-sectional area. Mastering these skills is essential for students and professionals in engineering and physics, as they... see moreapply to real-world scenarios involving fluid behavior in various systems. see less

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2. If a pipe narrows and the flow rate stays constant, the fluid speed increases.

True

False

Concept: area–speed tradeoff. Flow rate q = av. If a decreases, v must increase to keep q the same.

Explanation

Concept: area–speed tradeoff. Flow rate q = av. If a decreases, v must increase to keep q the same.

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3. Volume flow rate q is given by:

Q = p/ρ

Q = a·v

Q = m·g

Q = ρ/a

Concept: definition of q. For flow through an area, the volume per second equals cross-sectional area times average speed. This is a basic relationship used in many flow problems.

Explanation

Concept: definition of q. For flow through an area, the volume per second equals cross-sectional area times average speed. This is a basic relationship used in many flow problems.

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4. If q is constant, doubling area a makes speed v become ______ as large.

Concept: inverse relationship. With q fixed, v = q/a. Doubling a halves v.

Explanation

Concept: inverse relationship. With q fixed, v = q/a. Doubling a halves v.

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5. A pipe section has area 0.010 m² and speed 2.0 m/s. The flow rate is:

0.005 m³/s

0.020 m³/s

0.200 m³/s

2.010 m³/s

Concept: compute q = av. q = 0.010 × 2.0 = 0.020 m³/s. Units work out as m²·m/s = m³/s.

Explanation

Concept: compute q = av. q = 0.010 × 2.0 = 0.020 m³/s. Units work out as m²·m/s = m³/s.

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6. Continuity applies to gases too, but compressibility may matter at high speeds or large pressure changes.

True

False

Concept: compressible vs incompressible. Liquids are often treated as incompressible. Gases can change density, so the simple av constant form may need modification.

Explanation

Concept: compressible vs incompressible. Liquids are often treated as incompressible. Gases can change density, so the simple av constant form may need modification.

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7. In a steady flow of an incompressible fluid, mass flow rate is:

Always zero

Constant along the pipe

Only constant in wide pipes

Constant only if the pipe is vertical

Concept: conservation of mass. In steady flow, what enters per second must exit per second. That is conservation of mass.

Explanation

Concept: conservation of mass. In steady flow, what enters per second must exit per second. That is conservation of mass.

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8. If the speed increases in a narrower section, that does not automatically mean the pressure increases there.

True

False

Concept: speed and pressure can trade. In many ideal flows, higher speed is associated with lower pressure (Bernoulli idea). Real flows also include losses, but speed-up does not imply pressure-up.

Explanation

Concept: speed and pressure can trade. In many ideal flows, higher speed is associated with lower pressure (Bernoulli idea). Real flows also include losses, but speed-up does not imply pressure-up.

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9. If a river narrows but the same amount of water passes each second, the water speed usually:

Decreases

Increases

Stays exactly the same

Becomes zero

Concept: continuity in open flow. The same principle applies: smaller cross-sectional area means higher average speed to carry the same flow rate.

Explanation

Concept: continuity in open flow. The same principle applies: smaller cross-sectional area means higher average speed to carry the same flow rate.

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10. For steady incompressible flow, q is the same at every cross-section, so q = a·v = ______.

Concept: constant flow rate. Steady flow means no accumulation of fluid in any section. Therefore flow rate is the same throughout.

Explanation

Concept: constant flow rate. Steady flow means no accumulation of fluid in any section. Therefore flow rate is the same throughout.

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11. A pipe narrows from 6 cm diameter to 3 cm diameter (same fluid, steady). The speed in the narrow part is:

2× the wide part

4× the wide part

1/2 the wide part

1/4 the wide part

Concept: area scales with diameter². Area is proportional to d², so halving diameter reduces area by 4. To keep q constant, speed must increase by 4.

Explanation

Concept: area scales with diameter². Area is proportional to d², so halving diameter reduces area by 4. To keep q constant, speed must increase by 4.

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12. Continuity is essentially a statement that fluid is not created or destroyed in the flow (mass conservation).

True

False

Concept: conservation. For normal fluids, mass is conserved. Continuity is the mathematical expression of that idea for flowing fluids.

Explanation

Concept: conservation. For normal fluids, mass is conserved. Continuity is the mathematical expression of that idea for flowing fluids.

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13. If q = 0.030 m³/s and area is 0.015 m², speed is:

0.45 m/s

1.0 m/s

2.0 m/s

45 m/s

Concept: compute v = q/a. v = 0.030 / 0.015 = 2.0 m/s. Check units: m³/s divided by m² gives m/s.

Explanation

Concept: compute v = q/a. v = 0.030 / 0.015 = 2.0 m/s. Check units: m³/s divided by m² gives m/s.

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14. If a flow is unsteady (changing with time), q might not be the same at every cross-section at every instant.

True

False

Concept: unsteady flow. In unsteady flow, fluid can temporarily accumulate or empty from regions. That can make local flow rates vary with time.

Explanation

Concept: unsteady flow. In unsteady flow, fluid can temporarily accumulate or empty from regions. That can make local flow rates vary with time.

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15. Which assumptions help you use q = av easily?

Steady flow

Incompressible fluid (or nearly so)

Average speed across the area is meaningful

The pipe must be horizontal

Concept: when to apply. Horizontal is not required for continuity. The key is steady mass conservation and consistent density.

Explanation

Concept: when to apply. Horizontal is not required for continuity. The key is steady mass conservation and consistent density.

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16. A common reason flow slows in a wider section is that:

Wider means less mass

The same flow is spread over a larger area

Gravity turns off

Pressure becomes negative

Concept: area effect. With fixed q, larger area gives smaller v. This is a direct consequence of q = av.

Explanation

Concept: area effect. With fixed q, larger area gives smaller v. This is a direct consequence of q = av.

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17. For water in typical pipes, treating it as incompressible is usually reasonable.

True

False

Concept: incompressible approximation. Water’s density changes very little under everyday pressure changes. This makes incompressible models effective for many problems.

Explanation

Concept: incompressible approximation. Water’s density changes very little under everyday pressure changes. This makes incompressible models effective for many problems.

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18. If two pipes carry the same flow rate, the pipe with smaller area has:

Lower speed

Higher speed

The same speed always

No flow

Concept: speed vs area. v = q/a. Smaller a produces larger v for the same q.

Explanation

Concept: speed vs area. v = q/a. Smaller a produces larger v for the same q.

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19. Continuity can be used to predict changes in speed without knowing the fluid’s viscosity.

True

False

Concept: geometry + conservation. Continuity comes from mass conservation and geometry. Viscosity affects pressure losses, but not the basic q = av relation for steady incompressible flow.

Explanation

Concept: geometry + conservation. Continuity comes from mass conservation and geometry. Viscosity affects pressure losses, but not the basic q = av relation for steady incompressible flow.

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20. Grade 9 wrap-up: if you know the flow rate and one cross-section’s area, the most reliable next step to find speed is to:

Use temperature

Use v = q/a and keep units consistent

Assume v is constant everywhere

Multiply q by a

Concept: using definitions carefully. q = av is a definition for volumetric flow rate. Rearranging correctly and checking units prevents common mistakes.

Explanation

Concept: using definitions carefully. q = av is a definition for volumetric flow rate. Rearranging correctly and checking units prevents common mistakes.

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