Question

Ideal fluid flows along a flat tube of constant cross-section, located in a horizontal plane and bent as shown in figure above (top view). The flow is steady. Are the velocities of the fluid equal at points 1 and 2?

• A. Velocity at point 1 is less than velocity at point 2.
• B. Velocity at point 1 is more than velocity at point 2.
  
• C. Velocity at point 1 is equal to velocity at point 2.
  
• D. Can't be determined.
  

Answer 1

The correct option is B Velocity at point 1 is more than velocity at point 2.

In the figure, between 1 and 2 fluid-particle are nearly circular motion and have centripetal acceleration. The force for this acceleration, like for any other situation in an ideal fluid, can only come from the pressure variation along the line joining 1 and 2. This required that pressure at 1 should be less than the pressure at 2.

$P_1<P_2$.

So, the fluid particle can have required acceleration. If there is no turbulence, then the motion can be taken as irrotational.

$\int \overrightarrow{v}.\overrightarrow{dl}=0$ (for closed-loop)

The velocity at point 1 is greater than the velocity at point 2

$v_1>v_2$

The correct option is B.