IIIF Color HighRes
National Institute of Informatics - Digital Silk Road Project
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| IIIF Color HighRes |
| Scientific Results of a Journey in Central Asia, 1899-1902 : vol.1 |
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| Vertical section of River. |
Citation Information
30
THE TARIM RIVER.
of sounding. Denote these successive mean velocities by vI, v„ v3, v,t_I.
Fig. 34 shows a vertical section of the river at a place of measurement. Then the
vertical lines 117, 0,, N,O„ Nn_= On_= indicate the lines of sounding, and the
dotted lines MIP=, M,P„ /14_2 On_. bisect the distances between them. The
A Nt M, N2 Me Ns Mn-? Nn-1
P
Fig. 34.
most accurate way to ascertain the volume of the water flowing past the section in the unit of time is to measure with the planimeter the areas of the figures AM=PI,
MI M, P, PI, and to muliply the successive areas by their corresponding mean
velocities and take the sum of the products. Thus, if we denote the areas by
aI, a„ a3, an_I, then the volume Q which passes the section in the unit of time is
Q = alvl+a,v,+ +an_Ivn_I=.Zav (I)
The mean depth is
dm = b (2)
where A = aI + a, + + an = Za (3)
A denoting the area of the total section of the river.
The mean velocity of the entire river is
U _Zav_ Q
m
2a A
As a check upon this, Q may be calculated from the formula
Q = bdm v m (5)
II.
The following simplified method may also be employed, without any material error, more especially as the contours of the river-bottom between the vertical soundings are not known.
In fig. 35 we bisect each of the n divisions ANI, NI N„ .... Nn_I B, and from the points of bisection QI, Q„ .... Qn let drop the perpendiculars QIRI, Q,R,S„ .... QnRn; then through the lower ends OI, O„ .... On_I of the lines of sounding draw the horizontal lines RI R2 S2 R3, .... Sn_IRn. Then the area of the figure bounded by the broken line QI RI R, S, R3 S3 .... Sn _ I Rn Qn and the straight line QIQn is approximately equal to the area of the vertical section of the river; and the difference diminishes without limit, as the number of points NI, N„ .... Nn _ I
On-y On.-1
(4)
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