FBISE, NCP & NBF-aligned resources for Classes 9–12
Browse by Class
Browse by Type
Physics Chapter 6 : Topic 4
Equation of Continuity
1 / 35
The equation of continuity is based on the principle of conservation of:
Reasoning: The continuity equation represents conservation of mass during fluid flow.
2 / 35
The equation of continuity for an incompressible fluid is:
Reasoning: $\mathbf{A}_{\mathbf{1\ }}\mathbf{v}_{\mathbf{1}}\mathbf{=}\mathbf{A}_{\mathbf{2\ }}\mathbf{v}_{\mathbf{2}}$ for constant density fluids.
3 / 35
The quantity $\mathbf{(Av)}$ in fluid flow represents:
Reasoning: $\mathbf{Q = Av}$ is the volume of fluid passing per second.
4 / 35
The continuity equation states that for steady flow:
Reasoning: The same amount of mass must pass through every cross-section per second.
5 / 35
For an incompressible fluid:
Reasoning: Constant density allows conservation of volume flow rate.
6 / 35
Water flowing through a narrow pipe section moves faster because:
Reasoning: Reduced area increases velocity to maintain flow rate.
7 / 35
According to continuity equation, if the cross-sectional area of a pipe decreases, fluid velocity:
Reasoning: $\mathbf{A}_{\mathbf{1\ }}\mathbf{v}_{\mathbf{1}}\mathbf{=}\mathbf{A}_{\mathbf{2\ }}\mathbf{v}_{\mathbf{2}}$ Smaller area requires greater velocity.
8 / 35
If the area of a pipe is doubled, the velocity of an incompressible fluid becomes:
Reasoning: $\mathbf{A}_{\mathbf{1\ }}\mathbf{v}_{\mathbf{1}}\mathbf{=}\mathbf{A}_{\mathbf{2\ }}\mathbf{v}_{\mathbf{2}}$ $\mathbf{\Longrightarrow}$ Velocity is inversely proportional to area.
9 / 35
In a pipe of varying cross-section, the fluid velocity is maximum where:
Reasoning: Smaller cross-sectional area produces higher velocity.
10 / 35
A fluid flowing from a wide pipe into a narrow pipe experiences:
Reasoning: Continuity requires increased velocity in narrower sections.
11 / 35
The general equation of continuity is:
Reasoning: General continuity equation includes density.
12 / 35
The equation $\mathbf{A}_{\mathbf{1\ }}\mathbf{v}_{\mathbf{1}}\mathbf{=}\mathbf{A}_{\mathbf{2\ }}\mathbf{v}_{\mathbf{2}}$ applies when:
Reasoning: It is valid for incompressible fluids.
13 / 35
If density changes during flow, the correct relationship is:
Reasoning: Mass conservation requires density consideration.
14 / 35
Continuity equation assumes that fluid flow is:
Reasoning: It applies to steady flow conditions.
15 / 35
If no fluid is added or removed from a pipe, the mass entering per second is:
Reasoning: Conservation of mass requires equal flow rates.
16 / 35
Water flows through a pipe of area $\mathbf{4\ }\mathbf{m}^{\mathbf{2}}$ with velocity $\mathbf{3\ m/s}$. The flow rate is:
Reasoning: $\mathbf{Q = Av}$ $\mathbf{\Longrightarrow}$ $\mathbf{Q = 4(3) = 12\ }\mathbf{m}^{\mathbf{3}}\mathbf{/s}$
17 / 35
A pipe has area $\mathbf{2\ }\mathbf{m}^{\mathbf{2}}$ and water velocity $\mathbf{5\ m/s}$. If the area becomes $\mathbf{1\ }\mathbf{m}^{\mathbf{2}}$, new velocity is:
Reasoning: $\mathbf{A}_{\mathbf{1\ }}\mathbf{v}_{\mathbf{1}}\mathbf{=}\mathbf{A}_{\mathbf{2\ }}\mathbf{v}_{\mathbf{2}}$ $\mathbf{\Longrightarrow}$ $\mathbf{2(5) = 1(}\mathbf{v}_{\mathbf{2}}\mathbf{)}$ $\mathbf{\Longrightarrow}$ $\mathbf{v}_{\mathbf{2}}\mathbf{= 10\ m/s}$
18 / 35
Water flows in a pipe with velocity $\mathbf{4\ m/s}$ through an area of $\mathbf{0.5\ }\mathbf{m}^{\mathbf{2}}$. The volume flow rate is:
Reasoning: $\mathbf{Q = Av}$ $\mathbf{= 0.5(4) = 2}\mathbf{\ m}^{\mathbf{3}}\mathbf{/s}$
19 / 35
A pipe diameter decreases from $\mathbf{10\ cm}$ to $\mathbf{5\ cm}$. The velocity becomes:
Reasoning: Area depends on diameter squared: $\mathbf{A \propto}\mathbf{d}^{\mathbf{2}}$Area decreases by factor $\mathbf{4}$, velocity increases $\mathbf{4}$ times.
20 / 35
A fluid moves from a pipe area of $\mathbf{8\ }\mathbf{m}^{\mathbf{2}}$ to $\mathbf{2\ m}^{\mathbf{2}}$. If initial velocity is $\mathbf{2\ m/s}$, final velocity is:
Reasoning: $\mathbf{8(2) = 2}\mathbf{v}_{\mathbf{2}}$ $\mathbf{\Longrightarrow}$ $\mathbf{v}_{\mathbf{2}}\mathbf{= 8\ m/s}$
21 / 35
Blood flows faster in narrow arteries because:
Reasoning: Continuity equation predicts higher velocity in smaller areas.
22 / 35
A nozzle attached to a hose increases water speed because:
Reasoning: Smaller area produces higher velocity.
23 / 35
The shape of an airplane wing involves fluid flow principles including:
Reasoning: Fluid velocity changes are related to pressure changes.
24 / 35
If a river becomes narrower, the water velocity generally:
Reasoning: Reduced cross-sectional area increases velocity.
25 / 35
A garden hose sprays water faster when the opening is partially closed because:
Reasoning: Smaller area increases speed.
26 / 35
Two pipes carry the same fluid. The pipe with smaller diameter has:
Reasoning: Velocity increases as area decreases.
27 / 35
If the velocity of fluid doubles, the area must become:
Reasoning: $\mathbf{Av = constant}$ Q28. The continuity equation cannot be applied directly if:A. Fluid is incompressible B. Flow is steadyC. Density changes significantly D. Pipe is narrowAnswer: CDensity changes require the general equation.
28 / 35
In steady flow, fluid particles:
Reasoning: Steady flow follows streamlines.
29 / 35
The continuity equation shows that:
Reasoning: It is derived from conservation of mass.
30 / 35
A pipe narrows suddenly. At the narrow section:
Reasoning: Smaller area requires greater velocity.
31 / 35
If the diameter of a pipe is reduced to half, the velocity becomes:
Reasoning: $\mathbf{A \propto}\mathbf{d}^{\mathbf{2}}$Half diameter means quarter area, so velocity becomes four times.
32 / 35
For the same fluid, continuity equation requires:
Reasoning: Volume flow rate remains constant.
33 / 35
The product of cross-sectional area and velocity has units of:
Reasoning: $\mathbf{m}^{\mathbf{2}}\mathbf{\times}$ $\frac{\mathbf{m}}{\mathbf{s}}\mathbf{=}\mathbf{m}^{\mathbf{3}}\mathbf{/s}$
34 / 35
A fluid cannot accumulate inside a steady pipe because:
Reasoning: Conservation of mass prevents accumulation.
35 / 35
The continuity equation is most useful for solving problems involving:
Reasoning: It relates velocity and area in fluid systems.
Your score is
Restart quiz
