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Consider a uniform U-tube with a diaphragm at the bottom and filled with a liquid to different heights in each arm (see Fig. 16-31). Now imagine that the diaphragm is punctured so that the liquid flows from left to right. (a) Show that the application of Bernoulli's equation to points 1 and 3 leads to a contradiction. (b) Explain why Bernoulli's equation is not applicable here. (Hint: Is the flow steady?)

Consider a uniform U-tube with a diaphragm at the bottom and filled with a liquid to different heights in each arm (see Fig. 16-31). Now imagine that the diaphragm is punctured so that the liquid flows from left to right. (a) Show that the application of Bernoulli's equation to points 1 and 3 leads to a contradiction. (b) Explain why Bernoulli's equation is not applicable here. (Hint: Is the flow steady?)

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
8 years ago
(a) It is given that the points 1 and 3 in the given U tube are at atmospheric pressure. This shows that the pressure at points 1 and 3 are equal. In accordance with Bernoulli’s equation, the speed of the flow of the liquid at the point 1 and 3 in the U tube should be same. This will make the level between the points 1 and 3 same. But it is given that the levels are not same. This contradicts Bernoulli’s equation.
(b) The liquid will start flowing in the U tube once the diaphragm is punctured. The liquid now flows from left to right. The flow of the liquid will not be steady or streamlined due to the shape of the U tube. Thus, Bernoulli’s equation cannot be used and the level of the liquid in points 1 and 3 are not the same.

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