Two fluid jets of equal crosssectional area collide to produ

Two fluid jets of equal cross-sectional area collide to produce a single, well-mixed, output stream as shown below. If the velocity of the horizontal input stream is 3m/s and the angle (theta) is found to be 30 degrees, determine the velocity of the vertical input stream. The net body forces in both the horizontal and vertical directions are zero.

Solution

As body forces on the fluid are zero, we can say that the Volumetric flow rate is conserved in both the vertical and horizontal directions. Also as the diameteres of both the input stream pipes are equal the angle made by the final velocity with X axis will be the same as the angle made by the resultant velocity of the two input stream velocities with the X axis.

Thus we have V₃ cos 30° = V₁ and V₃ sin 30° = V₂

===> V₃ *(3/2) = 3 ===> V₃ = 3.464 m/s

===> V₂ = 0.5 * V₃ = 1.732 m/s

Input velocity at pipe 2 is V₂ = 1.732 m/s