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Consider a uniform U-tube with a diaphra...

Consider a uniform U-tube with a diaphragm at the bottom and filled with a liquid to different heights in each limb as shown in Fig. Now imagine that the diaphragm is punctured so that the liquid flows from left to right. (a) Show that the application of Bernoulli's particle to points (1) and Diaphragm (2) leads to a constradiction. (b) Explain why Bernoulli's principle is not applicabe here

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To solve the problem step by step, we will analyze the situation using Bernoulli's principle and understand why it leads to a contradiction in this scenario. ### Step 1: Understanding the Setup We have a U-tube with a diaphragm at the bottom, filled with liquid to different heights in each limb. When the diaphragm is punctured, the liquid starts flowing from the left limb to the right limb. **Hint:** Visualize the U-tube and the liquid levels in both limbs before and after the diaphragm is punctured. ### Step 2: Applying Bernoulli's Equation ...
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Fluids at rest exert a normal force to the walls of the container or to the sruface of the body immersed in the fluid. The pressure exerted by this force at a point inside the liqid is the sum of atmospheric pressure and a factor which depends on the density of the liquid, the acceleration due to gravity and the height of the liquid, above that point. The upthrust acting on a body immersed in a stationary liquid is the net force acting on the body in the upward direction. A number of phenomenon of liquids in motion can be explain by Bernoulli's theorem which relates the pressure, flow speed and height for flow of an ideal incompressible fluid. A container of large uniform corss sectional area. A resting on a horizontal surface holds two immiscible, non viscous and incompressile liquids of densities d and 2d , each of height H//2 as shown in the figure. The lower density liquid is open to the atmosphere having pressure P_(0) . Situation II: A cyliner is removed and the original arrangement is restoreed.A tiny hole of area s(slt ltA) is punched on the veritical side of the containier at a height h(hltH//2) The height h_(m) at which the hole should be punched so that the liquid travels the maximum distance is

Fluids at rest exert a normal force to the walls of the container or to the sruface of the Body immersed in the fluid. The pressure exerted by this force at a point inside the liqid is the sum of atmospheric pressure and a factor which depends on the density of the liquid, the acceleration due to gravity and the height of the liquid, above that point. The upthrust acting on a body immersed in a stationary liquid is the net force acting on the body in the upward direction. A number of phenomenon of liquids in motion can be explain by Bernoulli's theorem which relates the pressure, flow speed and height for flow of an ideal incompressible fluid. A container of large uniform corss sectional area. A resting on a horizontal surface holds two immiscible, non viscous and incompressile liquids of densities d and 2d , each of height H//2 as shown in the figure. The lower density liquid is open to the atmosphere having pressure P_(0) . Situation I: A homogeneous solid cylinder of length L(LltH//2) . cross sectional area A//5 is immersed such that it floats with its axis vertical at liquid -liquid interface with lenght L//4 in the denser liquid. The density of the solid is

Fluids at rest exert a normal force to the walls of the container or to the sruface of the body immersed in the fluid. The pressure exerted by this force at a point inside the liqid is the sum of atmospheric pressure and a factor which depends on the density of the liquid, the acceleration due to gravity and the height of the liquid, above that point. The upthrust acting on a body immersed in a stationary liquid is the net force acting on the body in the upward direction. A number of phenomenon of liquids in motion can be explain by Bernoulli's theorem which relates the pressure, flow speed and height for flow of an ideal incompressible fluid. A container of large uniform corss sectional area. A resting on a horizontal surface holds two immiscible, non viscous and incompressile liquids of densities d and 2d , each of height H//2 as shown in the figure. The lower density liquid is open to the atmosphere having pressure P_(0) . Situation II: A cyliner is removed and the original arrangement is restoreed.A tiny hole of area s(slt ltA) is punched on the veritical sideof the containier at a height h(hltH//2) The horizontal distance x travelled by the liquid is

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