1148

THEORY AND PRACTICE OF ENGINEERING.

Book II.

maintained that it is not possibleto have too many float-boards,provided the wheel is not toomuch loaded witli them.

It may be readily understood,that when water acts by its mo-mentum only, the circumferenceof the wheel, instead of requir-ing buckets, as in the overshotwheel, is furnished with float-boards, which, exposed to theaction of running water, may-have its power increased by awell regulated fall; such a wheelmay communicate its force toany machinery. The figuresshow the method that Smeatonrecommended for the construc-tion of undershot wheels; thesluice or penstock is raisedor depressed by a ratchet andpinion ; the spur-wheel to drivethe machinery is shown restingon its bearings on the left of theelevation.

On Overshot Wheels, by

Smeaton _We now proceed to

examine the power and applica-

:in—

Fig 1738. PLAN OF UNDERSHOT WHEEL.

tion of water, when acting by its weight: we might at first be led to suppose, that the samequantity of water descending through the same perpendicular space would produce equalpower, when the machinery is freed from friction, and that if the height of a column ofwater be 30 inches, and its base or aperture 1 inch, every cubic inch that passes through theaperture would acquire the same momentum, a column of uniform pressure being alwaysmaintained, as one cubic inch let fall from the top will acquire in falling down to the levelof the aperture; but that this is not exactly the case, experiment has proved.

The alterations made in the .machinery we have already described were as follows: thesluice 16 (fig. 1733.) being shut down, the rod H I was unscrewed and taken off. Theundershot wheel was removed, and an overshot put in its place, of 2 inches in the depth ofthe bucket, and the number of buckets was thirty-six : the standards S and T were raisedhalf an inch, so that the bottom of the wheel might be clear of dead water; a trunk forbringing the water to the wheel was fixed according to the dotted lines f s. The ratchetoo not being of one piece of metal with the ferrule was with its catch turned to the con-trary side: the movable barrel acted by this means, although the water-wheel moved thecontrary way; the results were, head 6 inches; 14J strokes of the pump in a minute,12 do. =s 80 lbs.; weight of the scale being wet, lOj oz. ; counterweight for twenty turns,besides the scale, 3 oz. In the maximum experiment there were 20] turns in a minute,each of which raised the weight 4.J inches, or 93-37 inches in a minute; the weight in thescale was 1 9 pounds; the weight of the scale lO.j ounces: the counterweight three ouncesin the scale, making with the weight of the scale 20£ pounds, and which was the wholeresistance or load; this multiplied by 93*37 inches, gives 1914 for the effect.

The ratio of the power and effect is 2900 : 1914, or 10 : 6 -6, or as 3 to 2 nearly. If we,however, compute the power from the height of the wheel only, we shall have 96| lbs.multiplied by 24 inches, equal to 2320 for the power, and this will be to the effect as2320 : 1914, or as 10 : 8*2, or as 5 to 4 nearly.

On the most proper Height of the Wheel in proportion to the whole Descent. — We havealready observed that the effect of the same quantity of water descending through the sameperpendicular space is double, when acting by its gravity on an overshot wheel, to that pro-duced by the same when acting by its impulse upon an undershot: it also appears, thatby increasing the head from S inches to 11, that is, the whole descent from 27 to 35 inches,or in the ratio of 7 to 9 nearly, the effect is only in the ratio 8-1 to 8*4, that is as 7 to7*26 ; consequently, the increase of effect is not a seventh of the increase of perpendicularheight; hence, the higher the wheel is in proportion to the descent, the greater will be theeffect, as it depends less upon the impulse of the head, and more upon the gravity of thewater in the buckets.

The Velocity of the Circumference of the Wheel which produces the greatest Effect . — If abody be allowed to fall freely from the surface of the head to the bottom of the descent, itwill take a certain time in falling, and in that case the whole action of gravity is spent in