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Physics Chapter 6 : Topic 5
Flow Velocity in a Narrow Pipe
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When the end of a rubber pipe is squeezed, the water velocity increases because:
Reasoning: According to the continuity equation, decreasing area increases velocity to maintain constant flow rate. $\mathbf{\Longrightarrow}$ $\mathbf{A}_{\mathbf{1\ }}\mathbf{v}_{\mathbf{1}}\mathbf{=}\mathbf{A}_{\mathbf{2\ }}\mathbf{v}_{\mathbf{2}}$
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Squeezing a rubber pipe demonstrates the application of:
Reasoning: The phenomenon occurs due to conservation of mass in fluid flow.
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When the opening of a pipe is reduced, the same amount of water must pass through:
Reasoning: For steady flow, volume flow rate remains constant.
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The velocity of water increases at the squeezed end because:
Reasoning: Smaller cross-sectional area requires higher velocity.
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The relationship between area and velocity of an incompressible fluid is:
Reasoning: $\mathbf{Av = constant}$
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If the radius of the pipe opening is reduced, the velocity of water:
Reasoning: Smaller radius means smaller area, resulting in greater velocity.
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A gardener squeezes the end of a hose to spray water farther. The increased distance is due to:
Reasoning: Higher exit velocity gives water greater range.
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In a squeezed pipe, the volume flow rate:
Reasoning: Conservation of mass requires constant flow rate.
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The equation used to explain the increase in velocity at the squeezed end is:
Reasoning: The continuity equation relates area and velocity.
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A narrow section of a pipe has:
Reasoning: Fluid speed increases where the cross-sectional area decreases.
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Water flows through a pipe with area $\mathbf{4\ }\mathbf{m}^{\mathbf{2}}$ at $\mathbf{2\ m/s}$. If the squeezed area becomes $\mathbf{1\ }\mathbf{m}^{\mathbf{2}}$, velocity becomes:
Reasoning: $\mathbf{A}_{\mathbf{1\ }}\mathbf{v}_{\mathbf{1}}\mathbf{=}\mathbf{A}_{\mathbf{2\ }}\mathbf{v}_{\mathbf{2}}$ $\mathbf{\Longrightarrow}$ $\mathbf{4(2) = 1(}\mathbf{v}_{\mathbf{2}}\mathbf{)}$ $\mathbf{\Longrightarrow}$ $\mathbf{v}_{\mathbf{2}}\mathbf{= 8\ m/s}$
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A hose has an area of $\mathbf{6\ c}\mathbf{m}^{\mathbf{2}}$. When squeezed, the area becomes $\mathbf{2\ c}\mathbf{m}^{\mathbf{2}}$. If initial velocity is $\mathbf{3\ m/s}$, final velocity is:
Reasoning: $\mathbf{6(3) = 2}\mathbf{v}_{\mathbf{2}}$ $\mathbf{\Longrightarrow}$ $\mathbf{v}_{\mathbf{2}}\mathbf{= 9\ m/s}$
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If the area of a pipe opening is reduced to half, the velocity of water becomes:
Reasoning: $\mathbf{Av = constant}$ ; Halving area doubles velocity.
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A water jet becomes faster when passing through a nozzle because:
Reasoning: A nozzle reduces cross-sectional area.
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If the diameter of the pipe opening is reduced to half, velocity becomes:
Reasoning: Area depends on diameter squared. $\mathbf{\Longrightarrow}$ $\mathbf{A \propto}\mathbf{d}^{\mathbf{2}}$Half diameter gives one-fourth area, so velocity becomes four times.
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Why does water come out faster from a partially closed hose?
Reasoning: Reduced area increases velocity according to continuity equation.
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When a pipe is squeezed, which quantity remains constant?
Reasoning: Conservation of mass keeps mass flow rate constant.
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The velocity of water at the narrow end of a pipe is higher because:
Reasoning: The flow adjusts velocity to maintain continuity.
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If the end of a rubber pipe is squeezed completely closed:
Reasoning: A closed pipe prevents fluid movement.
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A fire hose nozzle increases water speed by:
Reasoning: Smaller area increases velocity.
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At the narrow section of a pipe, water generally has:
Reasoning: Continuity equation predicts increased speed at smaller areas.
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According to Bernoulli’s principle, where water velocity is higher, pressure is usually:
Reasoning: Higher speed regions have lower pressure.
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A squeezed pipe may produce a stronger water jet because:
Reasoning: Greater velocity increases kinetic energy of water.
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The increase in velocity at the squeezed end does $\mathbf{NOT}$ occur because:
Reasoning: Mass remains constant during flow.
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Two identical hoses carry water. One hose end is squeezed. The squeezed hose produces:
Reasoning: Smaller outlet area increases velocity.
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A pipe changes from a wide section to a narrow section. The product $\mathbf{(Av)}$:
Reasoning: $\mathbf{Av = constant}$ ; for incompressible steady flow.
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If the cross-sectional area of a pipe decreases by four times, velocity:
Reasoning: Velocity is inversely proportional to area.
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A nozzle attached to a water pipe works on the principle that:
Reasoning: Continuity equation explains nozzle operation.
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Squeezing a rubber pipe does not increase the amount of water supplied per second because:
Reasoning: The flow rate remains approximately constant.
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The main physics concept behind squeezing a pipe is:
Reasoning: Fluid adjusts velocity to maintain constant mass flow.
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