Chapter 11 : Applications of Viscous Flows Through Pipes
Lecture 37 :


Losses In Pipe Bends

  • Bends are provided in pipes to change the direction of flow through it. An additional loss of head, apart from that due to fluid friction, takes place in the course of flow through pipe bend.

  • The fluid takes a curved path while flowing through a pipe bend as shown in Fig. 37.2.             

Fig.  37.2 Flow through pipe bend

Whenever a fluid flows in a curved path, there must be a force acting radially inwards on the fluid to provide the inward acceleration, known as centripetal acceleration .

This results in an increase in pressure near the outer wall of the bend, starting at some point A (Fig. 37.2) and rising to a maximum at some point B . There is also a reduction of pressure near the inner wall giving a minimum pressure at C and a subsequent rise from C to D . Therefore between A and B and between C and D the fluid experiences an adverse pressure gradient (the pressure increases in the direction of flow).

Fluid particles in this region, because of their close proximity to the wall, have low velocities and cannot overcome the adverse pressure gradient and this leads to a separation of flow from the boundary and consequent losses of energy in generating local eddies. Losses also take place due to a secondary flow in the radial plane of the pipe because of a change in pressure in the radial depth of the pipe.

This flow, in conjunction with the main flow, produces a typical spiral motion of the fluid which persists even for a downstream distance of fifty times the pipe diameter from the central plane of the bend. This spiral motion of the fluid increases the local flow velocity and the velocity gradient at the pipe wall, and therefore results in a greater frictional loss of head than that which occurs for the same rate of flow in a straight pipe of the same length and diameter.

The additional loss of head (apart from that due to usual friction) in flow through pipe bends is known as bend loss and is usually expressed as a fraction of the velocity head as , where V is the average velocity of flow through the pipe. The value of K depends on the total length of the bend and the ratio of radius of curvature of the bend and pipe diameter R/D. The radius of curvature R is usually taken as the radius of curvature of the centre line of the bend. The factor K varies slightly with Reynolds number Re in the typical range of Re encountered in practice, but increases with surface roughness.