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#continuity equation

14 public questions tagged with this topic.

Fluid Pressure, Pascal's Law and Manometers

A spray tube (7cm2) has 35 holes of diameter 1.2mm. If the flow speed is 3.0m/min, what is the ejection speed?

A1v1 = A2v2, v1 = 3.0m/min = 0.05m/s, A1 = 7×10−4m2. Hole area: Ah = π(0.6×10−3)2, total A2 = 35×π×3.6×10−7≈3.958×10−5m2. v2 = 7×10−4×0.053.958×10−5≈0.884m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 0.9 m/s. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Surface Tension, Capillarity and Excess Pressure

A pipe narrows from 0.07m2 to 0.035m2. If water flows at 2.4m/s in the wider section, what is the speed in the narrower

Continuity equation: A1v1 = A2v2. A1 = 0.07m2, v1 = 2.4m/s, A2 = 0.035m2. v2 = A1v1A2 = 0.07×2.40.035 = 4.8m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 4.8 m/s. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Bernoulli's Theorem and Applications

A pipe’s cross-sectional area decreases from 0.04m2 to 0.01m2. If the speed at the larger end is 2.5m/s, what is the spe

Continuity equation: A1v1 = A2v2. A1 = 0.04m2, v1 = 2.5m/s, A2 = 0.01m2. v2 = A1v1A2 = 0.04×2.50.01 = 10m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 10 m/s. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Fluid Pressure, Pascal's Law and Manometers

A pipe’s cross-sectional area changes from 0.08m2 to 0.02m2. If the speed at the larger end is 1.2m/s, what is the speed

Continuity equation: A1v1 = A2v2. A1 = 0.08m2, v1 = 1.2m/s, A2 = 0.02m2. v2 = A1v1A2 = 0.08×1.20.02 = 4.8m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 4.8 m/s. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Surface Tension, Capillarity and Excess Pressure

A pipe narrows from 0.06m2 to 0.02m2. If water flows at 1.8m/s in the wider section, what is the speed in the narrower s

Continuity equation: A1v1 = A2v2. A1 = 0.06m2, v1 = 1.8m/s, A2 = 0.02m2. v2 = A1v1A2 = 0.06×1.80.02 = 5.4m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 5.4 m/s. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Surface Tension, Capillarity and Excess Pressure

A pipe’s cross-sectional area changes from 0.1m2 to 0.025m2. If water flows at 2.2m/s in the larger section, what is the

Continuity equation: A1v1 = A2v2. A1 = 0.1m2, v1 = 2.2m/s, A2 = 0.025m2. v2 = A1v1A2 = 0.1×2.20.025 = 8.8m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 8.8 m/s. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Surface Tension, Capillarity and Excess Pressure

A pipe’s cross-sectional area decreases from 0.09m2 to 0.03m2. If water flows at 1.5m/s in the larger section, what is t

Continuity equation: A1v1 = A2v2. A1 = 0.09m2, v1 = 1.5m/s, A2 = 0.03m2. v2 = A1v1A2 = 0.09×1.50.03 = 4.5m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 4.5 m/s. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Surface Tension, Capillarity and Excess Pressure

A spray tube (6cm2) has 30 holes of diameter 1.2mm. If the flow speed is 1.8m/min, what is the ejection speed?

A1v1 = A2v2, v1 = 1.8m/min = 0.03m/s, A1 = 6×10−4m2. Hole area: Ah = π(0.6×10−3)2, total A2 = 30×π×3.6×10−7≈3.39×10−5m2. v2 = 6×10−4×0.033.39×10−5≈0.531m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 0.53 m/s. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Viscosity, Stokes' Law and Reynolds Number

A pipe narrows from 0.12m2 to 0.04m2. If water flows at 1.6m/s in the wider section, what is the speed in the narrower s

Continuity equation: A1v1 = A2v2. A1 = 0.12m2, v1 = 1.6m/s, A2 = 0.04m2. v2 = A1v1A2 = 0.12×1.60.04 = 4.8m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 4.8 m/s. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Bernoulli's Theorem and Applications

Why does a fluid’s density remain nearly constant in streamline flow through a narrowing pipe?

The equation of continuity assumes the fluid is incompressible, meaning its density (ρ) remains constant, even as velocity increases in a narrowing pipe, ensuring mass conservation (Av = constant). As per NCERT, applying relevant law/formula with correct units and sign convention leads to Because the fluid is incompressible. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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