Fluid force/calculus question- why is the length in this integral what it is?
Hi, I'm supposed to find the fluid force on the vertical side of a tank, where the dimensions are given in feet. The tank is full of water and is in the shape of a trapezoid.
The length of the top part of the trapezoid is 4, while the length of the bottom side is 2. The tank is 3 ft. in height.
The soln manual gives me the following integral to find the fluid force:
F = weight of water (integral bounds) (height) (length) dy
F = 2 (62.4) (integral bounded between 3 and 0) (3-y) (y/3 + 1) dy
I understand everything about the integral except for how the length was determined. I realize that the top and bottom part of the trapezoid is different, but how do you get ( y/3 +1 ). Please do not hesitate to explain as if to a fifth grader. Thanks for your help!
wish i could draw a picture, but i'm sure you have one. the length is the variable length from side to side of the trapezoid, for a given fluid height of y (where y<=3). draw the trapezoid, and put in vertical dotted lines to represent the right triangles that compliment the square in the middle to make up the trapezoid... see what i mean? anyway, those right triangles are 3 high, 1 wide, sqrt(10) hypotenuse triangles.
so, at your given height, the horizontal leg of each of these right triangles is 1/3 the height, or y/3, right? (by similar triangles.) and you get two of those, plus the 2 in the middle, or ((2y)/3) + 2. BUT, your solutions manual factored out the two, it's at the beginning... so at the end you see (y/3) + 1.
hope that helped.
John Deere 670B 672B Motor Grader Parts Catalog LOTS More Manuals Listed PC-2063, CHAMPION MOTOR GRADER ROAD PARTS CATALOG MANUAL, CMI MOTOR GRADER AG-55 PARTS MANUAL, WABCO MOTOR GRADER 666 777 PARTS CATALOG MANUAL, CAT Caterpillar 140G Motor Grader Parts Manual Book catalog list 3306 oem 1986, CAT Caterpillar 14E Motor Grader Parts Manual Book 72G catalog spare shop list, CAT Caterpillar 14 Motor Grader Parts Manual 35F Book shop catalog spare list, CAT Caterpillar 120 Motor Grader Parts Manual Book 10R 22R catalog spare list, CAT Caterpillar 120 Motor Grader Parts Manual Book 89G 60H 1967 catalog spare OE, CAT Caterpillar 120 Grader Parts Manual Book 14K 35K catalog shop spare list OEM, CAT Caterpillar 12 Motor Grader Parts Manual Book catalog spare shop OEM 1963 8T, CAT Caterpillar 12 Grader Parts Manual Book catalog 6M catalog shop spare list, CAT Caterpillar 112 Motor Grader Parts Manual Book 82F catalog list spare shop, CAT Caterpillar 112 Motor Grader Parts Manual Book 3U 1963 catalog spare list, CAT Caterpillar 112 Motor Grader Parts Manual a Book 3U catalog shop spare OEM, CAT Caterpillar 12 Motor Grader Parts Manual Book 8T 1955 catalog shop spare OEM, CAT Caterpillar Parts Manual 14H Motor Grader w/3176C, GALLION 160L MOTOR GRADER PARTS MANUAL, 5 parts books manuals CATERPILLAR 950 no. 12 motor grader diesel 3406 engine , Simplicity Tractor OWNER & PARTS Manual GRADER BLADE 42, John Deere 670A & 672A Motor Grader Parts Catalog Manual jd, Caterpillar Cat 140H NA Motor Grader Parts Manual Set 2ZK1-up Feb 2001, CATERPILLAR CAT NO. 14G MOTOR GRADER PARTS MANUAL, 1966 WABCO 440 Motor Grader Parts Manual Catalog Serial No 8000 Machine J, Champion motor grader shop manual parts manual road grader D-560 D-686 D-600, Galion No 160 Motor Grader Parts List Book Manual, CATERPILLAR CAT NO. 16 MOTOR GRADER PARTS MANUAL, CATERPILLAR CAT NO. 14 MOTOR GRADER PARTS MANUAL, CATERPILLAR CAT NO. 14E MOTOR GRADER PARTS MANUAL, Lockwood Graders Parts & Instruction Manual with advertisement inside,
This entry was posted
on Sunday, October 18th, 2009 at 9:07 am and is filed under Construction.
You can follow any responses to this entry through the RSS 2.0 feed.
You can leave a response, or trackback from your own site.
Leave a Comment
You must be logged in to post a comment.