Physics · Bernoulli's principle and its applications
Three tubes and are connected to a horizontal pipe in which liquid is flowing. T
Three tubes \( A, B \) and \( C \) are connected to a horizontal pipe in which liquid is flowing. The radii of pipe at the joints of \( A, B \) and \( C \) are \( 2 c m, 1 c m \) and \( 2 c m \) respectively. The height of liquid:
- A. in A and B is equal
- B. in A is maximum
- C. \) in \( A \) and \( C \) is same
- D. is same in all three
Step-by-step solution
Bernoulli's principle for horizontal flow states that pressure + dynamic pressure is constant. The continuity equation (A1v1 = A2v2) shows that velocity is inversely proportional to cross-sectional area. Since area ∝ r^2, at B (r=1 cm) velocity is highest, so pressure is lowest, giving the smallest liquid height. At A and C (r=2 cm), velocities are equal, so pressures are equal, giving equal heights.
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