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Water flows through a horizontal tube as shown. The difference in heights of water columns is 5 cm. Areas of cross-section at points A and B are 6 cm² and 3 cm² respectively. Find the rate of flow of water. (g = 10 m/s²)

Options:
  1. $( \dfrac{200}{3} )$ cm³/s
  2. $( \dfrac{200}{6} )$ cm³/s
  3. $( \dfrac{200}{3} )$ cm³/s
  4. $( \dfrac{100}{3} )$ cm³/s

Solution:

From continuity equation: $[ 6V_A = 3V_B \Rightarrow V_B = 2V_A ]$ Using Bernoulli’s equation: $[ \rho gh = \frac{1}{2}\rho(V_B^2 - V_A^2) ]$ Solving: $[ V_A = \frac{100}{3}\ \text{cm/s} ]$ Flow rate: $[ Q = A_AV_A = \frac{200}{3}\ \text{cm}^3/s ]$ ✅ Correct Answer: (3)
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