Continuity Equation Basics Quiz: Test Fluid Flow Conservation

8th Grade

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| Questions: 20 | Updated: Mar 13, 2026

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1. For steady incompressible flow, volumetric flow rate q is:

Q = p/ρ

Q = a·v

Q = ρ·g·h

Q = m·g

Concept: definition of q. q measures volume per second passing through an area. For uniform average speed across area a, q = a times v.

Explanation

Concept: definition of q. q measures volume per second passing through an area. For uniform average speed across area a, q = a times v.

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About This Quiz

Continuity Equation Basics Quiz: Test Fluid Flow Conservation - Quiz

This assessment focuses on the Continuity Equation, a fundamental principle in fluid dynamics that describes the conservation of mass in fluid flow. It evaluates your understanding of key concepts such as fluid velocity, cross-sectional area, and mass conservation. Mastering these concepts is essential for engineers and scientists working with fluid... see moresystems, making this assessment a valuable tool for enhancing your knowledge in fluid dynamics. see less

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2. If q is constant, then a₁v₁ = a₂v₂.

True

False

Concept: continuity in two sections. Steady incompressible flow implies the same q at each cross-section. Therefore a₁v₁ = a₂v₂.

Explanation

Concept: continuity in two sections. Steady incompressible flow implies the same q at each cross-section. Therefore a₁v₁ = a₂v₂.

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3. A pipe narrows from area 0.020 m² to 0.010 m². If v₁ = 1.5 m/s, v₂ is:

0.75 m/s

1.5 m/s

3.0 m/s

6.0 m/s

Concept: a₁v₁ = a₂v₂. v₂ = (a₁/a₂) v₁ = (0.020/0.010)×1.5 = 3.0 m/s. Halving area doubles speed.

Explanation

Concept: a₁v₁ = a₂v₂. v₂ = (a₁/a₂) v₁ = (0.020/0.010)×1.5 = 3.0 m/s. Halving area doubles speed.

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4. If a increases while q stays the same, v must ______.

Concept: inverse relationship. v = q/a shows speed decreases when area increases. This is a direct outcome of mass conservation.

Explanation

Concept: inverse relationship. v = q/a shows speed decreases when area increases. This is a direct outcome of mass conservation.

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5. If q = 0.030 m³/s and a = 0.015 m², then v equals:

0.5 m/s

1.0 m/s

2.0 m/s

20 m/s

Concept: compute v = q/a. v = 0.030 / 0.015 = 2.0 m/s. Units check: (m³/s)/(m²) = m/s.

Explanation

Concept: compute v = q/a. v = 0.030 / 0.015 = 2.0 m/s. Units check: (m³/s)/(m²) = m/s.

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6. For incompressible flow in a single pipe, the volumetric flow rate is the same at every cross-section (steady).

True

False

Concept: constant q. With no leaks and no accumulation, the volume per second cannot change along the pipe. If it did, fluid would have to compress or pile up.

Explanation

Concept: constant q. With no leaks and no accumulation, the volume per second cannot change along the pipe. If it did, fluid would have to compress or pile up.

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7. If a circular pipe’s diameter is halved (steady incompressible), the area becomes:

Half

One quarter

Double

Four times

Concept: area scales with d². a ∝ d². Halving d makes a = (1/2)² = 1/4 of the original.

Explanation

Concept: area scales with d². a ∝ d². Halving d makes a = (1/2)² = 1/4 of the original.

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8. If diameter halves and q stays constant, average speed increases by a factor of 4.

True

False

Concept: speed scales inversely with area. If area becomes 1/4, speed must become 4 times larger to keep q the same. This is a common continuity scaling.

Explanation

Concept: speed scales inversely with area. If area becomes 1/4, speed must become 4 times larger to keep q the same. This is a common continuity scaling.

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9. A river narrows to half its cross-sectional area (same q). The speed becomes:

Half

Double

Four times

Unchanged

Concept: continuity in open flow. q = av still applies to average flow. If a halves, v doubles.

Explanation

Concept: continuity in open flow. q = av still applies to average flow. If a halves, v doubles.

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10. The symbol a in q = a·v represents cross-sectional ______.

Concept: variable meanings. a is the area perpendicular to the flow direction. Using consistent units is important for correct q calculations.

Explanation

Concept: variable meanings. a is the area perpendicular to the flow direction. Using consistent units is important for correct q calculations.

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11. A pipe splits into two branches with q₁ = 0.012 m³/s and q₂ = 0.008 m³/s. The upstream flow is:

0.004 m³/s

0.010 m³/s

0.020 m³/s

0.096 m³/s

Concept: flow addition at junctions. Conservation of mass gives q_in = q₁ + q₂. So q_in = 0.012 + 0.008 = 0.020 m³/s.

Explanation

Concept: flow addition at junctions. Conservation of mass gives q_in = q₁ + q₂. So q_in = 0.012 + 0.008 = 0.020 m³/s.

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12. Continuity alone cannot tell you the value of q; it relates q at different sections.

True

False

Concept: what continuity provides. Continuity gives relationships like a₁v₁ = a₂v₂. To find q itself, you usually need boundary conditions or energy/pressure information.

Explanation

Concept: what continuity provides. Continuity gives relationships like a₁v₁ = a₂v₂. To find q itself, you usually need boundary conditions or energy/pressure information.

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13. If speed is 4 m/s in a pipe of area 0.005 m², q is:

0.0008 m³/s

0.020 m³/s

0.80 m³/s

20 m³/s

Concept: compute q = av. q = 0.005 × 4 = 0.020 m³/s. Always check that m²·m/s gives m³/s.

Explanation

Concept: compute q = av. q = 0.005 × 4 = 0.020 m³/s. Always check that m²·m/s gives m³/s.

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14. Using 'average speed' in q = av is common because real velocity profiles may vary across the pipe.

True

False

Concept: average vs local speed. Real flows are faster in the middle and slower near walls. q = av uses the cross-sectional average velocity that gives the correct total flow.

Explanation

Concept: average vs local speed. Real flows are faster in the middle and slower near walls. q = av uses the cross-sectional average velocity that gives the correct total flow.

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15. Which statements are correct for steady incompressible flow?

Q is constant along a single pipe with no leaks

If a decreases, v increases

If v increases, a must increase

At a junction, q_in = sum of q_out

Concept: core continuity rules. a and v move in opposite directions for constant q. Junction flow rates add according to mass conservation.

Explanation

Concept: core continuity rules. a and v move in opposite directions for constant q. Junction flow rates add according to mass conservation.

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16. A nozzle reduces area to increase speed mainly because it:

Removes viscosity

Conserves flow rate while changing cross-section

Eliminates pressure

Makes fluid heavier

Concept: nozzle function. Nozzles reshape the flow area. With steady flow, a smaller area increases exit speed for the same volumetric rate.

Explanation

Concept: nozzle function. Nozzles reshape the flow area. With steady flow, a smaller area increases exit speed for the same volumetric rate.

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17. If the fluid is compressible and density changes, q may not stay constant even if mass flow rate does.

True

False

Concept: mass flow vs volume flow. Mass flow depends on density, while volume flow does not. If density changes, the same mass flow can correspond to different volume flows.

Explanation

Concept: mass flow vs volume flow. Mass flow depends on density, while volume flow does not. If density changes, the same mass flow can correspond to different volume flows.

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18. Which is the best statement about continuity for liquids in most classroom pipe problems?

Liquids always compress noticeably

Liquids are treated as incompressible, so q is constant if flow is steady and leak-free

Q must be zero

Speed is constant regardless of area

Concept: incompressible approximation. Water’s density changes very little in typical conditions. That makes the incompressible continuity equation accurate enough.

Explanation

Concept: incompressible approximation. Water’s density changes very little in typical conditions. That makes the incompressible continuity equation accurate enough.

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19. If a pipe suddenly expands, continuity still requires the same q before and after the expansion (steady, incompressible).

True

False

Concept: q continuity. Even if the speed changes, the same volume per second must pass both sections. Sudden expansions affect energy loss, but not mass conservation.

Explanation

Concept: q continuity. Even if the speed changes, the same volume per second must pass both sections. Sudden expansions affect energy loss, but not mass conservation.

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20. A student says, 'the fluid speeds up in a narrow section because pressure is higher there.' The best correction is:

Pressure is always higher in narrow sections

Continuity requires higher speed in smaller area for the same q

Narrow sections always stop flow

Speed depends only on temperature

Concept: separate continuity from energy. Continuity explains the speed change from geometry and mass conservation. Pressure can rise or fall depending on conditions, and needs additional principles to predict.

Explanation

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