A twodimensional reducing bend has a linear velocity profile

A two-dimensional reducing bend has a linear velocity profile at section 1. The velocity is uniform at section 2 & 3. Assume incompressible flow, find V_1, max. What are the x and y components of the velocity at section 3?

Solution

P=dsensity of liquid

A1= area of cross sections at 1=h1^2

A2= area if cross section at 2= h2^2

A3= h3^2

M1= mass of liquid coming at 1 in time DT

M1= p*A1*V1(Max)/2

M2= p*A2*V2

M3=p*A3*A3

As liquid is incompressible,

Then M1=M2+M3

h1^2*V1(Max)/2= (V2*h2^2+v3*h3^2)

V1(Max)=4000 ft/s

V3x= x components of v3= 80*cos40

V3y= y component of v3=80*sin40