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Water flows in a streamline motion through a horizontal pipe of circular cross-section as shown in the figure. The pressure difference of water between P and Q is 15 N m⁻². The areas of cross-section at P and Q are 40 cm² and 20 cm² respectively. The rate of flow of water through the pipe, in cm³ s⁻¹, is: [Take density of water =1000 kg m⁻³]

Asked in RE-NEET 2026 · Venturimeter and flow measurement

• (1) 400
• (2) 100
• (3) 200
• (4) 300

Step-by-step solution

Why the other options are wrong

• (2) 100 cm³ s⁻¹ needs v_P=0.025 m s⁻¹, which puts the Bernoulli drop at 1/2ρ(4-1)v_P²=0.94 N m⁻², not the 15 N m⁻² given
• (3) comes from pairing the speed at P with the area at Q: 20×10⁻⁴×0.1=2×10⁻⁴ m³ s⁻¹
• (4) 300 cm³ s⁻¹ needs v_P=0.075 m s⁻¹, which gives a pressure drop of 8.4 N m⁻², well short of 15

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