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