man, multiplied by his distance from the fulcrum, equals the weight at the other end times its distance from the fulcrum: The product of the man's weight by his distance from the fulcrum is his turning force. This product is what we call the torque. Torque means turning force. The product of weight in pounds times distance from fulcrum in feet is the torque in pound-feet. The torque of the man in this example is 600 pound-feet. The lever rule is that the total torque which tends to turn the lever in one direction equals the total torque which tends to turn it in the opposite direction. In the equation above we have left out of account the weight of the bar itself. Suppose the bar weighs 10 pounds. We must find where this weight is acting. To do this, lay the bar on the fulcrum, with no weight on it, and move it along until it balances. Now, the point where it balances is where the weight of the bar acts. This is called the center of gravity of the bar. Let us suppose it balances at the middle. The middle point of the bar is 12 feet from the fulcrum. This makes the turning force or torque of the bar itself 10 times 1%, or 15 pound-feet. This added to the turning force of the man makes the total turning force on the man's side of the fulcrum 615 pound-feet. The turning force on the other side must also be 615 pound-feet. But this turning force equals the weight times 1 foot. Hence the weight is 615 pounds. Fig. 13 shows a lever safety valve. The force which is trying to raise the valve is the pressure of the steam. The forces which are holding down the valve are the weight of the ball, the weight of the lever, and weight of valve and spindle. Now apply the lever rule. The turning force of the steam at blowing-off pressure equals the combined turning forces of the ball, lever, valve and spindle. The total pressure of steam equals pressure per square inch times area of valve. Turning force of ball equals weight of ball times distance from ball to fulcrum. FIG. 13. THE LEVER SAFETY VALVE. Turning force of lever equals weight of lever times distance from fulcrum to center of gravity of lever. Turning force of valve and spindle equals weight of valve and spindle times distance from fulcrum to center of valve. Let W weight of ball in pounds. V = weight of valve and spindle in pounds. L 1 distance between fulcrum and center of ball in inches. distance between fulcrum and center of valve in inches. g distance between fulcrum and center of gravity of lever in inches. AP area of valve in square inches. pressure of steam, in pounds per square inch, at which valve opens. Then, turning force of steam equals PAI and turning force of ball, lever and valve, taken together, equal WL+vl+ wg. Therefore: In practice, g may be taken as one-half the length of the lever. The fulcrum is the bolt which passes through the end of the lever. To find steam pressure at which valve will open, divide both sides of the above equation by Al. This gives P WL+vl+wg which means that blowing-off pressure equals combined turning forces of lever, valve and ball, divided by area of valve times distance from fulcrum to center of valve. Example: Weight of ball W 76 pounds. Weight of valve and spindle v 4 pounds. Distance between fulcrum and center of ball L 20.15 inches. Distance between fulcrum and center of valve 1 2 inches. lever Distance between fulcrum and center of gravity of When gauge reads 65, valve will open. To find where the ball must be placed so that valve will open at a certain pressure: L is the quantity to be found. In the equation PAI WL+vl+wg, transpose v 1 and w g. This gives PA1-v1-wg WL. Divide by W. This gives With the same safety valve as in the last example, find where the ball must be placed so that the valve will open at 60 pounds pressure. Center of ball must be 18.4 inches from the fulcrum. 81-96 névén. in all three parts taken together; we have 225 square inches. So we have used the total number of square inches that we had to begin with, and we have made a square, each side of which measures 25 inches. Therefore, the square root of 625 is 25. This gives us the Rule for Finding Square Root. Divide the number into periods of two figures each, beginning with units. Find the largest square in the left-hand period. Subtract this square from the lefthand period and place its square root in the answer. Bring down and annex the next period; call this the remainder. Take twice the part of the answer already found as a trial divisor. Find how many times the |