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Water flows in steady streamline motion through a tube whose axis is horizontal. Consider two points A and B located in the tube at the same horizontal level. Which statement about the pressures at A and B is correct?

1. The pressures at A and B are equal for any shape of the tube.
2. The pressures are never equal.
3. The pressures are equal if the tube has a uniform cross-section.
4. The pressures may be equal even if the tube has a non-uniform cross-section.

Correct answer: The pressures may be equal even if the tube has a non-uniform cross-section.

Solution

At equal height, Bernoulli gives P + (1/2)*rho*v² = constant. Pressures are equal only when speeds are equal, i.e., when the cross-sections at A and B are equal. This can happen even in a non-uniform tube if A and B happen to have the same area. So the pressures may be equal even for a non-uniform tube.

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