Measure Flow Rates in Open Channel such as Flumes and Irrigation Ditches

Figure 3.20 (p. 124) Rectangular, sharp-crested weir geometry.

Figure 3.21 (p. 126) Representation of the energy line and the hydraulic grade line.

HGL vs. EGL For stationary bodies such as reservoirs or lakes, EGL and HGL coincide with the free surface of the liquid. EGL is always a distance V2/2g about the HGL. The two lines converges when velocity decreases and diverges when velocity increases. Mechanical energy loss due to frictional effects causes the EGL and HGL to slope downward in the direction of flow.

(a)The energy line and hydraulic grade line for flow from a tank, (b) discharge from a reservoir through a diffuser, (c) idealized Bernoulli type flow

Fluid Kinematics Fluid Kinematics deals with describing the motion of fluids without necessarily considering the forces and moments that cause the motion. Lagrangian description (following a fluid particle) Eulerian description (flow field)

Lagrangian Description With a small number of objects, such as billiard Balls on a pool table, individual objects can be tracked. Newton’s laws are used to obtain the momentum and kinetic energy exchanged

Difficulties with Lagrangian Description Fluid particles can not be easily defined or identified as fluid particles move around Fluid is a continuum, interactions between particles are not easy to describe Fluid parcels continuously deform as they move Nevertheless, many practical applications of involving tracking a passive scalars in a flow, rarefied gas dynamics calculations concerning of reentry of a spaceship into the earth’s atmosphere, development of flow measurement based on particle imaging.