Theoretical Studies Concerning the Hydropulse

Cover Theoretical Studies Concerning the Hydropulse
Theoretical Studies Concerning the Hydropulse
James Johnston Stoker
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82 . 069 1. 57 . 84 . 068 7 = 1. 1 '1 ~ ° V = 0. 5 ° f v^= . 01 V. = 3 1. 373 . 302 1. 366 . 301 7 = 1. 3 v^ = v„= . 416 v^= . 024 ^1 ~ -^ 1. 198 . 570 1. 188 . 566 CONFIDENTIAL 46 COMPIDENTIAL A3 the table shows, the approximate formula appears to be quite accurate over a wide range of parameter values.
In the following table a few conparlsons of exact and approximate values for the time of stroke dimensionless form, cf. Section 4) are given: T3 (in Cases Time of Stroke Tg Approximate Exact 7
...= 1. 1 Vj^ = . 01 Vg = 0. 5 v;. O v; = 3 . 353 . 148 . 392 . 150 7 = 1. 3 v^ = . 024 V3 = . 416 v; = o vl=l . 319 . 248 . 370 • 259 As remarked above, the approximate formula for the time of t stroke becomes more accurate when the initial velocity (v.
in dimensionless form) increases.
As we have seen in the preceding section, our formula for I_ gives an upper bound for this quantity. The formula s for t_, as we have seen, furnishes a lower bound, and consequently the formula for P_ yields an upper bound.


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