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Reply to two queries in the last number of the Journal of the Franklin Institute, respecting the comparative effect and value of different falls of Water
Reply to two Queries in the last number oj lin Institute, respecting the comparative fall* of Water.
:
TO THE ]~DITOR 0¥ TIlE JOUlt~AI* OF THE FR&NKLI]g INSTITUTE.
(_"
Sm,--In No. 2, Vol. 8, of your Journal, a subscriber propounds the following queries, viz. 1st. How many inches of water under 15 feet fall will produce the same effect as 100 inches under a 20 feet fall, both acting on overshot wheels under a S feet head? 2nd. Suppose 100 inches of water of 20 feet 6 inches fall, be received at 600 dollars per annum, what will be the value of 100 inches, the fall being 9 feet 8 inches, the situation being otherwise equal? , To which it is believed the following observations are applicable. The power of water, to produce mechanical eflhct, is as its perpendicular fall, the true measure of which is found by multiplying its weight by its fall; but the best devised modes of applying it will not produce equal effects in equal portions of its fall. For example, takethe circumstances of query 1st, the fall 20 feet, acting under 3 feet head, which for convenience I shall divide into 3 feet head and 17 feet fall. It has been found that the greatest effect, in relation to the power of water acting by gravity on a wheel, is as 8 is to 10, and that the head, or that portion of the descent from the surface of the water in the reservmr to the point where it impinges on the wheel, is as 1 is to 7. (See Smeaton's Experimental Inqmry, pages 81 and 52.) By applying these data to the circumstances of query lsti Wd hcve the following calculations anti results. Suppose 100 tons of water to descend from the reservoir tO the top of the wheel 36 inches × 100 = 3600 power, the effect will be as i to 7, ~ = 514.28 Descent on the wheel 17 feet = ~04 inches "} ' ! × 100 = 20400 power, the efihct' wdl" be], . : ~it65~0~:::~, as 8 to 10, . j . '.., ~ ~:,~i,',!(",:~,~ Effect of 100 tons of w ater under ~0 feet fail ~ i ~ a 4:!~~8 To find the effect under 15 feet tall, divided into 5 feet head/and 12 feet fall. Head 56 inches x 100 == 5600 power, the ~ = 514:28 effect is as 1 to 7, Fall, 144 inches × 100 = 14400 power~the effect as 8 to 10, = 11520. Effects of 100 tons under 15 feet fall,
Effect.
12054.£8
Inches.
As 16854.28 ~ 100 : : 12054.28 : 189.9 inches, answer to query 1st. Query 2nd. 'I he annual value of 9 feet 8 inches thll, compared with ~0 feet 6 inches fall, will depend in some measure on the method of
214 Comparative Effect of Different Falls of Water, its application. The results of three different modifications are el. hibited in the annexed calculations. 1st, 20 feet 6 inches head and fall to be applied to an overshot wheel under 3 feet head. Suppose 100 tons of water to descend from the reservoir to th~ top of the wheel, 36 inches × 100 := 3600 power, the ett~ct as I to 7~ ~ ~- 514.~8 Descent on the wheel ~10inches × 100 = f 21000~ effect as 8 to 10~ . = 16800. Effect of 20 feet 6 inches fall~ 17314.~8 9 feet 8 inches fall~ to be applied to an overshot wheel under 3 feet head. Head .~6 inches × 100 = 3600 power, the~ eithct as 1 to 7, ) ~- 514.~8 Fall, 80 inches × 100 ~- 8(100 power, the t = 6400. effect as 8 to 10~ Either. of 9 feet 8 inches fall, on an overshot wheel, 6914.~s ~2nd. If 9 feet 8 inches lhll be applied to a wheel 14 feet diameter under 5 feet head, that is, with the gate 4 inches below its horizon. tal centre, it is believed that the best method of applying the water, is, to direct it in a tangent to that point of the wheel where the bucket shall receive it, which will be (if the opening shall be ~ inches wide,) about 18 inches below the gate; the impiugiu~ point will then be at the bottom of the bucket~ 14 inches below, (it that be the depth of the bucket.) Thus arranged, the head and tall will oe, From the top of the water to the gate, 36 inches. From the gate to the receiving, point~ 18 From the receiving to the impinging point, 14 .... 68 head. From the impinging point to bottom of wheel~ 48 fall. Head and fall, 116 Eft~ct of the head relative to the power in this last arrangement will be as l is to 6. Suppose 100 tons of water desceml to the impinging point 68 inches X 1 0 0 ~ 6800, the eflhct as 1 to 6 = 11S5.33 Descent on the wheel 48 inches × 100 = 4800, the effect as 8 to 10 = 3840. ~97S.S3 $d. The same as 2nd, with centre buckets in. place of close buckets, t4 inches deep. In this case the impinging point will be 18 inches below the gate. Head and fall thus: to the gate, 55 inches. From the gate to the impinging point, 18 From the last point to the bottom of the wheel,
54 head. 69. fall.
~ e m a r k s on ¢2rnott's Elements o f Physics. 100 tons x 54 ~ 5400 power, the effect as 1 to 6 = t00 tons × 6 s = 6200 power, the effect as t~ to 10 ~
~15
900 I~ ":! 4960
Eft'ect of 9 f e e t 8 inches fall on breast wheel with centre buckets, 5860 As 1 7 5 1 4 . 2 8 : 600 dollars : : 69t4.£8 : [~£5,%85, value of 9 feet 8 inches f a l l , overshot. As 17514.c28 : 600 dollars : : 4975.55 : ~17£.88~value of breast, buckets 1 4 inches deep. As 1 7 5 1 4 . ~ 8 : 600 dollars : : 5860 : $~05.7, value of centre buckets. The d e p t h of the shrouding is always lost from the fall on overshot wheels, a n d as the loss is greater in proportion on small than on large wheels, ( u ~ l e s s the shrouding be narrower in proportion asthe wheel is smaller,) the 6 feet 8 inch wheel will fall something sh~rt of the result a s s i g n e d to it in the calculation. A~OTHrR SNZsscr,~s~.
~ ' 0 R T H ~ ,TOUR-N,kL O P T I t ~ P n k N K L I N
Remarks o n Jlrnott's Elements of Physics.
INSTITUTe.
By a Correspondent.
THE ~ E l e m e n t s of Physics, or Natural Philosophy, General and Medieal,'~ l a t e l y republished by Messrs. Carey, Lea &Carey, under the e d i t o r s h i p of Dr. Hays, is a treatise well ftted to serve the purposes o f those who have not leisure to peruse works con C~ruc~ted on the p l a n o f rigorous demonstration. To many readers, a knowledge of l e a d i n ~ facts, and. g.eneral principles, .is .more . .interesting than p u r e l y sc~enttfie d~scusswns. Conversation, even m auxed assemblies, often turns on these great outlines of science. Fir the purposes o f general society, therefore, their acquisition mu~ be ~endered a s e~sy as possible'. At the same time, then, that We sh'~Uiit deprecate t h e substitution of vague,- discursive reading, f0rdili~ht stu@, in t h e ph.ysico-mathematical sciences, among the classes"of our various seminaries, we ought to rejoice at every efibrt whid~ makes t h o s e sciences accessible and available to the mass Of mat~kind~ To this e n d are directed the establishment 0f public:le¢~ii~esg!~ publication o f popular treatises, the 'institution or" praetieM~Sci~[S~ and the c i r c u l a t i o n of journals for the disseminatioh of useful :~k:n~w-~ ledge. The m e d i c a l profession of our country will be under, particular obligations f o r the republication of this interesting v01uin'z~~ T h e word ph3cslclan, as generally applied, has often proved a Curious misnomer, i n being ~ppropriated to those who have no knowledge ~of "physics~'" lueea~ a non lueendo, and doctor a non doeendo, or a non doeto. . Dr. A r n o t t ' s division o f his work, is, on the whole, jUdicious~ his facts and illustrations well selected; his explanationssimple and intelligibIe, a n d his style lucid and familiar. His m e t h o d of presenting the several subjects, might, perhaps, be improved b y placing his. general~ statements. . on what. he .calls the " a n a l y s e s , " at the end, instead of the begznmng of his sections, and .
:
TO THE ]~DITOR 0¥ TIlE JOUlt~AI* OF THE FR&NKLI]g INSTITUTE.
(_"
Sm,--In No. 2, Vol. 8, of your Journal, a subscriber propounds the following queries, viz. 1st. How many inches of water under 15 feet fall will produce the same effect as 100 inches under a 20 feet fall, both acting on overshot wheels under a S feet head? 2nd. Suppose 100 inches of water of 20 feet 6 inches fall, be received at 600 dollars per annum, what will be the value of 100 inches, the fall being 9 feet 8 inches, the situation being otherwise equal? , To which it is believed the following observations are applicable. The power of water, to produce mechanical eflhct, is as its perpendicular fall, the true measure of which is found by multiplying its weight by its fall; but the best devised modes of applying it will not produce equal effects in equal portions of its fall. For example, takethe circumstances of query 1st, the fall 20 feet, acting under 3 feet head, which for convenience I shall divide into 3 feet head and 17 feet fall. It has been found that the greatest effect, in relation to the power of water acting by gravity on a wheel, is as 8 is to 10, and that the head, or that portion of the descent from the surface of the water in the reservmr to the point where it impinges on the wheel, is as 1 is to 7. (See Smeaton's Experimental Inqmry, pages 81 and 52.) By applying these data to the circumstances of query lsti Wd hcve the following calculations anti results. Suppose 100 tons of water to descend from the reservoir tO the top of the wheel 36 inches × 100 = 3600 power, the effect will be as i to 7, ~ = 514.28 Descent on the wheel 17 feet = ~04 inches "} ' ! × 100 = 20400 power, the efihct' wdl" be], . : ~it65~0~:::~, as 8 to 10, . j . '.., ~ ~:,~i,',!(",:~,~ Effect of 100 tons of w ater under ~0 feet fail ~ i ~ a 4:!~~8 To find the effect under 15 feet tall, divided into 5 feet head/and 12 feet fall. Head 56 inches x 100 == 5600 power, the ~ = 514:28 effect is as 1 to 7, Fall, 144 inches × 100 = 14400 power~the effect as 8 to 10, = 11520. Effects of 100 tons under 15 feet fall,
Effect.
12054.£8
Inches.
As 16854.28 ~ 100 : : 12054.28 : 189.9 inches, answer to query 1st. Query 2nd. 'I he annual value of 9 feet 8 inches thll, compared with ~0 feet 6 inches fall, will depend in some measure on the method of
214 Comparative Effect of Different Falls of Water, its application. The results of three different modifications are el. hibited in the annexed calculations. 1st, 20 feet 6 inches head and fall to be applied to an overshot wheel under 3 feet head. Suppose 100 tons of water to descend from the reservoir to th~ top of the wheel, 36 inches × 100 := 3600 power, the ett~ct as I to 7~ ~ ~- 514.~8 Descent on the wheel ~10inches × 100 = f 21000~ effect as 8 to 10~ . = 16800. Effect of 20 feet 6 inches fall~ 17314.~8 9 feet 8 inches fall~ to be applied to an overshot wheel under 3 feet head. Head .~6 inches × 100 = 3600 power, the~ eithct as 1 to 7, ) ~- 514.~8 Fall, 80 inches × 100 ~- 8(100 power, the t = 6400. effect as 8 to 10~ Either. of 9 feet 8 inches fall, on an overshot wheel, 6914.~s ~2nd. If 9 feet 8 inches lhll be applied to a wheel 14 feet diameter under 5 feet head, that is, with the gate 4 inches below its horizon. tal centre, it is believed that the best method of applying the water, is, to direct it in a tangent to that point of the wheel where the bucket shall receive it, which will be (if the opening shall be ~ inches wide,) about 18 inches below the gate; the impiugiu~ point will then be at the bottom of the bucket~ 14 inches below, (it that be the depth of the bucket.) Thus arranged, the head and tall will oe, From the top of the water to the gate, 36 inches. From the gate to the receiving, point~ 18 From the receiving to the impinging point, 14 .... 68 head. From the impinging point to bottom of wheel~ 48 fall. Head and fall, 116 Eft~ct of the head relative to the power in this last arrangement will be as l is to 6. Suppose 100 tons of water desceml to the impinging point 68 inches X 1 0 0 ~ 6800, the eflhct as 1 to 6 = 11S5.33 Descent on the wheel 48 inches × 100 = 4800, the effect as 8 to 10 = 3840. ~97S.S3 $d. The same as 2nd, with centre buckets in. place of close buckets, t4 inches deep. In this case the impinging point will be 18 inches below the gate. Head and fall thus: to the gate, 55 inches. From the gate to the impinging point, 18 From the last point to the bottom of the wheel,
54 head. 69. fall.
~ e m a r k s on ¢2rnott's Elements o f Physics. 100 tons x 54 ~ 5400 power, the effect as 1 to 6 = t00 tons × 6 s = 6200 power, the effect as t~ to 10 ~
~15
900 I~ ":! 4960
Eft'ect of 9 f e e t 8 inches fall on breast wheel with centre buckets, 5860 As 1 7 5 1 4 . 2 8 : 600 dollars : : 69t4.£8 : [~£5,%85, value of 9 feet 8 inches f a l l , overshot. As 17514.c28 : 600 dollars : : 4975.55 : ~17£.88~value of breast, buckets 1 4 inches deep. As 1 7 5 1 4 . ~ 8 : 600 dollars : : 5860 : $~05.7, value of centre buckets. The d e p t h of the shrouding is always lost from the fall on overshot wheels, a n d as the loss is greater in proportion on small than on large wheels, ( u ~ l e s s the shrouding be narrower in proportion asthe wheel is smaller,) the 6 feet 8 inch wheel will fall something sh~rt of the result a s s i g n e d to it in the calculation. A~OTHrR SNZsscr,~s~.
~ ' 0 R T H ~ ,TOUR-N,kL O P T I t ~ P n k N K L I N
Remarks o n Jlrnott's Elements of Physics.
INSTITUTe.
By a Correspondent.
THE ~ E l e m e n t s of Physics, or Natural Philosophy, General and Medieal,'~ l a t e l y republished by Messrs. Carey, Lea &Carey, under the e d i t o r s h i p of Dr. Hays, is a treatise well ftted to serve the purposes o f those who have not leisure to peruse works con C~ruc~ted on the p l a n o f rigorous demonstration. To many readers, a knowledge of l e a d i n ~ facts, and. g.eneral principles, .is .more . .interesting than p u r e l y sc~enttfie d~scusswns. Conversation, even m auxed assemblies, often turns on these great outlines of science. Fir the purposes o f general society, therefore, their acquisition mu~ be ~endered a s e~sy as possible'. At the same time, then, that We sh'~Uiit deprecate t h e substitution of vague,- discursive reading, f0rdili~ht stu@, in t h e ph.ysico-mathematical sciences, among the classes"of our various seminaries, we ought to rejoice at every efibrt whid~ makes t h o s e sciences accessible and available to the mass Of mat~kind~ To this e n d are directed the establishment 0f public:le¢~ii~esg!~ publication o f popular treatises, the 'institution or" praetieM~Sci~[S~ and the c i r c u l a t i o n of journals for the disseminatioh of useful :~k:n~w-~ ledge. The m e d i c a l profession of our country will be under, particular obligations f o r the republication of this interesting v01uin'z~~ T h e word ph3cslclan, as generally applied, has often proved a Curious misnomer, i n being ~ppropriated to those who have no knowledge ~of "physics~'" lueea~ a non lueendo, and doctor a non doeendo, or a non doeto. . Dr. A r n o t t ' s division o f his work, is, on the whole, jUdicious~ his facts and illustrations well selected; his explanationssimple and intelligibIe, a n d his style lucid and familiar. His m e t h o d of presenting the several subjects, might, perhaps, be improved b y placing his. general~ statements. . on what. he .calls the " a n a l y s e s , " at the end, instead of the begznmng of his sections, and .