#pipe flow

Fluid Pressure, Pascal's Law and Manometers

Water flows through a horizontal pipe at a speed of 3m/s with a pressure of 1.5×105Pa. If the speed increases to 6m/s, w

Using Bernoulli’s equation: P1+12ρv12 = P2+12ρv22 (height constant). P1 = 1.5×105Pa, v1 = 3m/s, v2 = 6m/s, ρ = 1000kg/m3. P2 = P1+12ρ(v12−v22) = 1.5×105+12×1000(9−36). P2 = 1.5×105−13500 = 1.365×105Pa.

Ref: NCBI Bookshelf, Ideal Gas Law: P1V1/T1 = P2V2/T2.

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Fluid Pressure, Pascal's Law and Manometers

What happens to the fluid velocity when a pipe narrows, assuming steady flow?

The equation of continuity (Av = constant) for an incompressible fluid in steady flow implies that as the cross-sectional area decreases, the velocity must increase to maintain a constant mass flow rate.

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

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Surface Tension, Capillarity and Excess Pressure

Why does a fluid’s viscosity contribute to energy loss in real flow systems?

Viscosity causes internal friction between fluid layers, converting kinetic energy into heat through shear stress, leading to energy dissipation, which Bernoulli’s ideal flow neglects. As per NCERT, applying relevant law/formula with correct units and sign convention leads to It converts kinetic energy to heat. 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 fluid flows through a pipe with speeds v1\=2m/s at height h1\=1m and v2\=4m/s at h2\=0m. If P1\=1.2×105Pa, find P2. (ρ

Bernoulli’s equation: P1+12ρv12+ρgh1 = P2+12ρv22+ρgh2. P1 = 1.2×105, v1 = 2m/s, h1 = 1m, v2 = 4m/s, h2 = 0m. Left: 1.2×105+12×1000×4+1000×10×1 = 1.2×105+2000+10000 = 1.32×105. Right: P2+12×1000×16 = P2+8000. 1.32×105 = P2+8000, P2 = 1.24×105Pa.

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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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

Water flows through a pipe of area 0.05m2 at 1.5m/s. What is the speed in a section of area 0.015m2?

Continuity equation: A1v1 = A2v2. A1 = 0.05m2, v1 = 1.5m/s, A2 = 0.015m2. v2 = A1v1A2 = 0.05×1.50.015 = 5m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 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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Bernoulli's Theorem and Applications

A pipe’s cross-sectional area decreases from 0.15m2 to 0.05m2. If water flows at 1.8m/s in the larger section, what is t

Continuity equation: A1v1 = A2v2. A1 = 0.15m2, v1 = 1.8m/s, A2 = 0.05m2. v2 = A1v1A2 = 0.15×1.80.05 = 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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