The document discusses flow through circular pipes. It considers a horizontal pipe of radius R with a fluid element of radius r sliding through the viscous fluid. An equation is derived for the velocity profile by equating shear stress and rate of deformation. The equation contains an integration constant C which is determined using the boundary condition that velocity is 0 at the pipe wall (r=R). This allows determining the maximum velocity Umax at the center of the pipe (r=0). The flow rate per second through an elementary ring is also defined. Finally, the drop in pressure over the length of the pipe is mentioned.

1. UNIT II
By
Dr. A. Asha, Prof/Mech
Kamaraj College of Engineering & Technology
FLOW THROUGH CIRCULAR PIPES

2. FLOW THROUGH CIRCULAR PIPES

3. FLOW THROUGH CIRCULAR PIPES
• Consider a horizontal pipe of radius “R”
• Consider a fluid element of radius “r” sliding in the viscous fluid with
a thickness dr

4. FLOW THROUGH CIRCULAR PIPES
Equation 9.1

5. FLOW THROUGH CIRCULAR PIPES

6. FLOW THROUGH CIRCULAR PIPES

7. FLOW THROUGH CIRCULAR PIPES
Integrating the above equation with respect to r
Equation 9.2

8. FLOW THROUGH CIRCULAR PIPES
• Where C is a constant and the
value is obtained using the
boundary condition
• When u=0, r =R,
Substituting the value of C in equation
9.2
Equation 9.3

9. FLOW THROUGH CIRCULAR PIPES
• The Velocity is maximum when
r= 0
• The maximum velocity Umax
• The fluid flowing/sec through
the elementary ring is

10. FLOW THROUGH CIRCULAR PIPES

11. FLOW THROUGH CIRCULAR PIPES

12. FLOW THROUGH CIRCULAR PIPES
• Drop of pressure over the length of the pipe

13. FLOW THROUGH CIRCULAR PIPES