Mechanics of Fluids

126 The principles governing fluids in motion
Fig. 3.23
✷
Since
�h = p1 − p2
ϱ fg
the volumetric flow rate is obtained by substituting in the relation
�
2g�h
Q = CA0
1 − (Ao/A1) 2
�1/2 = 0.62 × π
�
6
4 100 m
� �
2
2 × 12 500 N · m−2 0.86 × 103 kg · m−3 ×[1− (6/12) 4 ]
= 0.00976 m 3 · s −1
Hence
� 1/2
m = ϱ fQ = 0.86 × 10 3 kg · m −3 × 0.00976 m 3 · s −1 = 8.39 kg · s −1
3.7.5 Notches and sharp-crested weirs
A notch may be defined as a sharp-edged obstruction over which flow of a
liquid occurs. As the depth of flow above the base of the notch is related to
the discharge, the notch forms a useful measuring device. It is formed in a
smooth, plane, vertical plate and its edges are bevelled on the downstream
side so as to give minimum contact with the fluid. The area of flow is most
commonly either rectangular or V-shaped. A large rectangular notch is more
often termed a sharp-crested weir.
The pattern of flow over a notch is quite complex. Owing to the curvature
of the streamlines (Fig. 3.23) there is no cross-section of the flow over which
the pressure is uniform. Any attempt, therefore, to discover analytically
the relation between the rate of flow and the depth at the notch can be
based only on drastic simplifying assumptions. It is nevertheless useful in