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Question

Consider the following statements regarding thermal stratification and coriolis forces:

1. Thermal stratification refers to the layering of fluid elements that occur due to the density gradient created by changes in temperature.

2. Thermally stratified layers can make the flow irrotational from rotational.

3. An originally irrotational flow may become rotational due to the presence of coriolis forces.

Which of the above statements is/are correct?

The correct answer is
1, 2 and 3

Thermal Stratification Definition

The first statement correctly defines thermal stratification as the layering of fluid elements caused by density gradients resulting from temperature variations. This phenomenon is crucial in understanding fluid behavior in various environments.

Stratification Effects on Flow Rotation

Statement 2 suggests that thermally stratified layers can influence the rotational nature of a flow, potentially making it less rotational. Stable thermal stratification inhibits vertical fluid motion due to buoyancy effects. This suppression of vertical movement can dampen turbulence and complex rotational eddies, leading to more ordered, layered flow patterns. Thus, it can reduce the overall rotational character of the flow.

Coriolis Forces and Flow Rotation Induction

Statement 3 addresses the impact of Coriolis forces. These forces act on objects moving within a rotating frame of reference. An originally irrotational flow can become rotational if introduced into a rotating system where Coriolis forces act. For example, fluid moving radially on a rotating platform experiences a Coriolis force ($ \vec{F}_c = 2m (\vec{\Omega} \times \vec{v}) $) that deflects its path, inducing curvature and thus rotation.

Correct Statements Assessment

Evaluating the statements:

  • Statement 1 is a correct definition of thermal stratification.
  • Statement 2 is correct; stable stratification tends to suppress rotational turbulence.
  • Statement 3 is correct; Coriolis forces can induce rotation in initially irrotational flows.

All three statements (1, 2, and 3) are accurate descriptions of the phenomena.

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Important Questions from Fluid Properties

  1. In the context of fluid flow, which of the following statement(s) is/are correct?
  2. A water jet discharging from a $4 \ cm$ diameter orifice has a diameter of $3.5 \ cm$ at its vena contracta. The coefficient of velocity is defined as the ratio of the actual velocity of the jet at vena contracta to the theoretical velocity of the jet. If the coefficient of velocity is $0.98$, the coefficient of discharge for the orifice will be______________.  (rounded off to two decimal places).

  3. What is the force needed to apply to a piston of 2 cm radius in order to result a force of 8000 N at the working piston of radius 8 cm?
  4. What does specific gravity of liquids represent?
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