Zaymiey

⚛️ Physics  ·  Mechanical Properties of Fluids  ·  NEET & JEE

Two holes are at depths h<sub>1</sub> and h<sub>2</sub> from the water surface of a tank. Their ranges on the ground are equal. The relationship is:

Answer: h 1 + h 2 = H (total tank height).

  • A h<sub>1</sub> + h<sub>2</sub> = H (total tank height)
  • B h<sub>1</sub> = h<sub>2</sub>, meaning the two holes are at the same depth
  • C h<sub>1</sub> × h<sub>2</sub> = H², an incorrect product relation with the tank height
  • D h<sub>1</sub> = 2h<sub>2</sub>, an arbitrary fixed ratio between the two depths

Correct answer: A. h<sub>1</sub> + h<sub>2</sub> = H (total tank height)

Explanation: Range = 2√(h(H-h)). For equal ranges: h<sub>1</sub>(H-h<sub>1</sub>) = h<sub>2</sub>(H-h<sub>2</sub>). This holds when h<sub>1</sub> and h<sub>2</sub> are symmetric about H/2, i.e., h<sub>1</sub> + h<sub>2</sub> = H.

Continuity Equation: Narrow Pipe → Faster FlowA₁, v₁ (wide, slow)A₂, v₂ (narrow, fast)A₁v₁ = A₂v₂ (continuity)Smaller area → higher speed → (by Bernoulli) LOWER pressure

Since the same volume of fluid must pass every cross-section per second (continuity), the fluid speeds up where the pipe narrows; Bernoulli's equation then says this faster-moving fluid has lower pressure - the principle behind a venturi meter and an aircraft wing's lift.

Concept context

Pressure, buoyancy, Bernoulli equation, viscosity, and surface tension.

Read the full Mechanical Properties of Fluids notes →