456 APPLIED MECHANICS 
that the water level is lowered 4 feet in 4 minutes. What is the coefficient 
of discharge ? = 
23. A weir 20 feet long has a head of 15 inches above the crest. Taking the 
coefficient =0°6, calculate the discharge in cubic feet per second. 
24. Assuming that the weir of the preceding exercise has two end c 
tractions, calculate the discharge, in cubic feet per second, by Francis’s form 
25. A rectangular weir with one end contraction is required to dischai 
500,000 gallons of water per hour with a still-water head of 10 inches. Deter- 
mine the necessary length of the weir. Use Francis’s formula, 
26. Find the quantity of water which will flow through a notch 9 fee 
long, the head of water over the sill being 10 inches, and the area of the app 
channel being 30 square feet. [Inst.C. 
27. Water flows from a pond over a weir 10 feet long, to a depth of 10 inch 
it then flows along a level rectangular channel 8 feet broad, and over a seco 
weir the width of the channel, its crest being 1 foot above ‘the bottom. Fi 
the depth of the water over the 8-foot weir. [Inst.C. 
28. What are the advantages and disadvantages attending the use of 
V-gauge notch, and for what purposes is it specially suitable? The still-wai 
surface level is at a height of 15:5 inches above the bottom of a right-angled 
V-gauge notch. Calculate the discharge in cubic feet per second, taking 0°6 as 
the coefficient of discharge. 
29. A measuring weir is constructed with a 90° angular notch, the edges 
being bevelled to 45° on the outside to a nearly sharp edge. Give the formula — 
you think best for the discharge over such a weir, and apply it to calculate the 
discharge in gallons per minute when the water depth above the apex of the 
angular notch is 9°36 inches, and the water level 5 feet back from the weir — 
is found to be 0-93 inch above that of the weir. [Inst.C E] 
30. A triangular notch, having an angle of 90 degrees, is bs to measure 
the flow ofastream. Read- 
ings at intervals of 1 hour 
are taken, as shown in the | Reading 1 2 3 4 5 
table. 
Draw a curve showing | Head, in inches 4 5 6 7 6 
the rate of discharge at any 
time, and show how you ; 
would determine the discharge between the time of the first and last ae i ] 
nst 
31. Water flows over a rectangular. notch 3 feet wide to a depth of 6 inches, 
and afterwards passes through a triangular right-angled notch, Find the depth ~ 
of water through this notch. The coefficients of discharge for the notches are 
to be taken as 0°62 and 0°59 respectively. 
32. A weir at the edge of a pond is 6 feet wide. The crest of the weir is — 
6 inches below the water level of the pond, and 3 inches below the tail-water — 
level. Compute the discharge over this weir, in gallons per hour, if the co- 
efficient of discharge k=0°58. 
395. Loss of Energy or Head due to Sudden Enlargement of 
Pipe.—Let a straight horizontal pipe (Fig. 749) suddenly enlarge in 
cross section from an area a, at A’B’ to an i 
area a. In passing from the smaller to the | ¥ 
larger part of the pipe the stream lines will be ; 
disturbed, and eddies will be formed as shown, F cc 
but at some distance forward in the enlarged A kya = 
part of the pipe the motion will again become a ae 
steady and the stream lines parallel. Where = 5 
the eddies form there is a churning of the ae 
water, and a consequent loss of energy. . F —e 
Consider a portion of water between the D 
sections AB and CD, the motion being steady Fig. 749. 
at these sections. . Let this mass of water move forward to the position 
