Q1: In two dimensional flow the components of velocity are given by u = ax; v = by. The stream lines will be

ANS:C - hyperbolic

In the context of fluid dynamics or flow visualization, a hyperbolic flow pattern refers to a flow configuration where the streamlines resemble hyperbolas. Hyperbolic flow patterns are common in certain situations where fluid dynamics are complex, such as flows around bodies, jets, and wakes. Here are a few key points about hyperbolic flow patterns:

1. Shape of Streamlines: In hyperbolic flow, the streamlines exhibit the shape of hyperbolas. Hyperbolas are geometric curves with two distinct branches that extend indefinitely. In fluid flow, these hyperbolas represent the paths followed by fluid particles over time.
2. Occurrence: Hyperbolic flow patterns often arise in scenarios where there are significant changes in velocity or flow direction. For example, in the wake region behind an object moving through a fluid, the flow can exhibit hyperbolic patterns due to the interaction of the object's wake with the surrounding flow.
3. Complex Flow Dynamics: Hyperbolic flow patterns typically occur in regions of flow where there are strong gradients in velocity, pressure, or vorticity. These regions often exhibit complex flow dynamics characterized by swirling, mixing, and recirculation of fluid.
4. Applications: Understanding hyperbolic flow patterns is crucial in various engineering and scientific fields. Engineers and researchers study hyperbolic flows to analyze aerodynamic characteristics of aircraft, optimize designs of vehicles, understand fluid-structure interactions, and develop efficient mixing and heat transfer processes in industrial applications.