A pump which receives water directly from the mains at 20 pounds pressure, delivers 800 pounds of water per minute against a pressure of 300 pounds per square inch, through 1500 feet of straight pipe, the friction head being 358 per 1000 feet of pipe. Compute the horse-power required. 14. Compute the horse-power of a pump having four singleacting plungers each 4 inches in diameter, the length of stroke being 6 inches, the suction lift 15 feet, the pressure developed 200 lbs., the friction head 400, with 150 strokes per minute. 15. A pump with water plungers 61⁄2 inches in diameter delivers 247 gallons per minute, the stroke being 10 inches, and the r.p.m. 43. Compute the number of plungers in the pump with no allow ances. 16. A pump delivers 3000 gallons per minute through 2000 feet of 10-inch pipe against 300 pounds pressure, the suction lift being 15 feet. Determine the friction head from the table, and compute the horse-power. Size Pipe. 10" TABLE 151 FRICTION HEAD Friction Head in Feet per 1000 Feet of Straight Pipe. G.P.M. 700 750 800 900 1000 1200 1400 1600 From H. R. Worthington's " Turbine Pumps." CHAPTER XIII SOLUTION OF AN EQUATION SECTION 1. THE FOUR FUNDAMENTAL OPERATIONS. SECTION 2. ONE UNKNOWN QUANTITY. SECTION 3. TWO UNKNOWN QUANTITIES. SECTION 4. FORMULAS. SECTION 5. THE QUADRATIC. § 1. THE FUNDAMENTAL OPERATIONS 317. What the Operations Are. It is impossible to learn much about the solution of equations without a knowledge of the four fundamental operations, Addition, These are called fundamental because they underlie all other operations and are constantly used in all parts of mathematics. 318. Kinds of Terms. pression are of two kinds: The terms of an algebraic ex (1) Like, or numerical terms and those having one or more letters the same with the same exponents. (2) Unlike, all other terms. Thus in 3x+2x-8+5x2-6x2+9 5x2 and 3x are unlike terms because while the letters are the same, the exponents are different. 354 3x and 2x are like terms and 5x2 and -6x2 are like terms, because they have the same letters with the same exponents. 9 and 8 are also like terms because both are numerical. 319. Addition. The terms of an expression are added by adding the coefficients of the like terms. Thus the terms of the expressions 5+4x2+x and 3x+2x-8+5x2-6x2+9 are added by adding the x terms, the x2 terms, and the numerical terms as follows: x+4x2+5 3x+5x2-8 2x-6x2+9 6x+3x2+6 We therefore have the following: Addition Laws: (1) Write like terms in the same vertical column. 320. Examples. Add the terms in the following examples: 1. 2x3-x+5+2x2, 3+2x+x3-x2, x2-5+x3-3x. 2. 3b2-4+2b-b4, 3b-12b1-2b2+1, 3+4b—8b4. 3. 5ay+3cx-24, -5cx+12-3ay, 2cx+ay−3. 5. 50r-3+16v2+19s, −12v2 −25r−3+34s. 6. 10a2x-8ax2+3b2c, 42ax2-15a2x-8b2c. 7. 4√x +3√ÿ −6√t, −2√y+4√t‐2√x. 8. 5√x+y−2√x−y+12√x+y, 8√x−y+7√x + y −9√x−y• 9. 5b√x+1−3d√x−1+15, 6d√x−1−8+3b√x+1. 10. 3x2y3-14x3y +5, 17x2y −x2y3 −4. 321. Subtraction. When one expression is to be subtracted from another, it may be indicated by a minus sign between the two expressions, or by the words from and take. The names used in subtraction are as follows: (1) The minuend, or the quantity or expression from which subtraction is to be made. (2) The subtrahend, or the expression to be subtracted. Subtraction Laws. Following are the laws of subtrac tion: (1) Write like terms in the same column. (2) Change signs of all terms in the subtrahend. (3) Set down the excess of plus or minus under each column. 323. Inclosure of Subtrahend in Parenthesis. A subtrahend is frequently denoted by inclosing the quantities in a parenthesis preceded by a minus sign. Thus 3x36x2+12-(2x3+3x2+20) means exactly the same as though it were written, from 3x36x2+-12 take 2x3+3x2+20. The quantities in the parenthesis are therefore the subtrahend, and the parenthesis may be removed provided the signs of all the terms in the parenthesis are changed. Thus 3x3-6x2+12-2x3-3x2-20. . 324. Examples. Remove the following parentheses and add the terms: 1. 5b3+2y-ax2+8−(3y-2ax2+4−3b3) 2. 18x4-5y3 +21 −6x2y2 − (13+2y3 +8x1 −3x2y2) 3. 50x3-40x3y3+8-12x2-(4+21x3y3-3x2+20x3) 4. 3864-25x3b2-17x2b3-20-(17b4-14x3b2+8x3b3 −1) 325. Multiplication. One expression may be multiplied by another by the use of the following Laws of Multiplication. Thus (1) Like signs give plus; unlike signs give minus. (3) Bring down letters. (4) Add exponents of same letters. 3x3+2x2+5x-6 2x +3 6x4+4x2+10x2-12x 9x3+6x2+15x-18 6x4+13x3+16x2+3x-18 326. Examples. Perform the following multiplications: 1. 5x3+8x2-2x by 3x+4 2. 10y4-3y3+5y2-y by 8y2+2y 3. 12d2d2+16d-4 by 3d+2 4. 1123-42-11a2r3 by 32-2x |