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Where is the equals key?

That's a good question. There is no equals key on a RPN calculator. RPN stands for reverse "Polish" notation which uses the Lukasiewicz logic. This logic uses a stack for the operations of the calculator. A stack is simply a list of numbers and unit abbreviations arranged one on top of the other. The operations such as add, subtract, multiply, and divide are accomplished using the bottom two numbers and units on the stack. Any operation that only requires one argument, such as a trigonometric operation, uses the bottom most number and unit for the operation. In either case the result of the operation is placed back on the stack in the bottom most position. The first 5 of the examples below show the operation of the stack or RPN calculator.NOTE: For all the examples below, uncheck the NumPad operators copy directly to the Display selection under General Preferences in Calculator | Preferences from the menu of the calculator. To do this Click the Calculator menu selection, then Click the Preferences selection and the Preferences dialog box will appear. Find the General Preferences section of the Preferences and make sure that the box beside the NumPad operators copy directly to the Display does not have a check mark in it. All preferences will be saved as they were when the calculator program is closed.

  1. What is the sine of 30.5?
  2. Multiply 2.35 by 5.76.
  3. How many meters square will a 1 acre plot of land contain? How many feet will this be?
  4. How many miles per hour is the speed of light.
  5. How many miles in 26 miles and 360 yards.
  6. How many pounds force are represented in 5 kN plus 500 lbf?
  7. A hydraulic cylinder has a bore of 60 mm and a 25 mm rod. If the oil flow into the cylinder is 10 GPM, how fast does the cylinder extend and how fast does it retract?
  8. 250 SUS oil is flowing through a 1 in schedule 40 pipe at a flow rate of 189 liters per minute, what is the Reynolds number?
  9. What is the velocity head of the above flow?
  10. If the friction factor is 0.03, what is the head loss per 1ft of pipe?
  11. A pump has an overall efficiency of 90%. The maximum pressure that the pump will produce is 10.24 Mpa and the flow rate is 10 GPM, what size electric motor must be used to drive it in hp and kW?
  12. A 3 kW motor is turning at 150 RPM, what is the torque output in in-lbf and N-m?
  13. How many gallons of water fall on a 10 acre field for a 1 inch rainfall?
  14. A small field is 350 feet wide by 500 feet long, if the pump used for irrigating the field will produce 25 GPM, how long must the field be watered to produce the equivalent of a 1 inch rainfall?
  15. How many acres are in the above lawn?
  16. A bicycle tire is 70 cm in diameter, how many revolutions are needed to go 1 mile?
  17. A tensile force of 500 lbf is placed on a 35 mmdiameter bar, what is the normal stress in Mpa?
  18. A steel shaft is subjected to a 175 N-m torque. The allowable shear stress is 30 ksi, what is the smallest diameter in inches for this shaft?
  19. What is the force on a gear tooth if 2 hp are being transmitted at 1000 RPM and the pitch diameter is 110 mm?
  20. A corn bin is 24 ft in diameter. If 5500 bu of corn are to be put in the bin, how deep will the corn be in ft?
  21. What is the volumetric displacement of a gear pump where the root diameter of the gears is 75 mm, the OD is 95 mm, and the width of the gears is 1.15 inches. Find VD in liters per minute.
  22. If this pump has a volumetric efficiency of 95% and the speed is 750 RPM, how much flow will be produced in GPM?
  23. What is the pressure in psi and MPa on a diver in the ocean at a depth of 150 m.
  24. A hydraulic pump has a maximum pressure rating of 1500 psi and a rated flow of 15.6 GPM. If a 220 V motor is to drive the pump, what is the approximate current that the motor will draw at full power?

1. What is the sine of 30.5°?

Equation: sin(30.5° )=? Solution:
  • Type 30.5deg (NOTE: Type 30.5deg means to enter the numbers and letters from the keyboard of the computer just as they appear after the word Type)
  • Click the sin button.
  • Answer 0.50753836 NOTE: The number format and number of decimal points shown may be changed by clicking the right mouse button when the cursor is over the entry edit box on the calculator. When a change is made, all the numbers in the stack will change as well. Try this by right clicking on the edit box and selecting Number Format from the menu. Now change the number of decimal places or select another number format. Also notice the other options available.
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2. Multiply 2.35 by 5.76.

Solution:
  • Type 2.35 <ENTER> ( NOTE: <ENTER> means Press the <ENTER> key on the computer or Click the ENTER button on the calculator. In a two argument operation, the first number must be placed on the stack before keying in the second number. This is done by pressing the <ENTER> key. For a one argument operation the <ENTER> key press may be omitted)
  • Type 5.76 then Press * (or Click the multiply button on the calculator).
  • Answer 13.53600000.
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3. How many meters square will a 1 acre plot of land contain? How many feet will this be?

Equation: Image Solution: (AutoConv and SI selected)
  • Type acre <ENTER> (NOTE: A unit abbreviation entered alone means that one (1) is assumed)
  • Display 1.000000 Acre.
  • Click Imagebutton on the calculator.
  • Answer 63.61491 m.
  • Type ft, Press the F11 function key (NOTE: The F11 function is the short cut key for performing conversions)
  • Answer 208.71033 ft
  • Alternate method using the Units Selector dialog:
  • Type 1 <ENTER>
  • Click the Select Units button on the calculator, then Click the Area tab from the Units Selector dialog to show the units available on the Area page. Click the Acre button, then OK.
  • Display reads 1.000000 Acre.
  • Click Imagebutton on the calculator.
  • Answer 63.61491 m.
  • Click the Convert button and the Units Selector dialog is entered again. This time the units selected will be used for the conversion.
  • Select the Length page and Click the ft button, then OK.
  • Answer 208.71033 ft
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4. How many miles per hour is the speed of light.

The speed of light is c= 299 792 458 m s^-1 (From the NIST Web site. URL http://physics.nist.gov. IMPORTANT: To use this number in UniSolver™, the units must be separated in one of the following ways: m-sec^-1, m*sec^-1, or m/sec. Also, seconds must be abbreviated as sec, otherwise there will be a message "Problem with Units" displayed. If this occurs, correct the units and Press <ENTER> again. This number will not copy using the clipboard.
Solution: (Select Scientific number format and 8 Places)
  • Type 299792458m-sec^-1 or 2.99792458e8m/sec or 2.99792458x108m*sec^-1 <ENTER>
  • Display 2.99792458E+8 m/sec (If Scientific number format and 8 Places has been selected)
  • Click the Convert button. Select the Length page.
  • Make sure that the Numerator button is selected in the lower left corner.
  • Click the mi button.
  • Click the Denominator button. (All subsequent unit selections will be in the denominator. To switch back to the Numerator click the Numerator button again. In this way a series of units may be assembled)
  • Click the Time page, then Click the hr button. The edit box should read mi/hr.
  • Click OK.
  • Answer 6.70616629E+8 mi/hr or 1.86282397E+5 mi/sec
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5. How many miles in 26 miles and 360 yards.

Equation: Image Solution:
  • Type 26mi <ENTER>
  • Type 360yd, Press + (or click the + button on the calculator)
  • Answer 26.2045455 mi. NOTE: If the entry is reversed, the answer will be 46120.0000000 yd.
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6. How many pounds force are represented in 5 kN plus 500 lbf?

Equation: Image Solution:
  • Type 500lbf <ENTER>
  • Type 5kn, Press + (or click the + button on the calculator)
  • Answer 1624.04472 lbf. NOTE: If the entry is reversed, the answer will be 7.22411 kN.
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7. A hydraulic cylinder has a bore of 60 mm and a 25 mm rod. If the oil flow into the cylinder is 10 GPM, how fast does the cylinder extend and how fast does it retract?

Equations: Image Solution: (AutoConv and US selected)
  • Type 10gpm <ENTER>
  • Type 60mm, Double Click Area (NOTE: Double Click means to click the left mouse button twice in quick succession)
  • Type 25mm, Double Click Area
  • Press – (minus key on keyboard or on the calculator)
  • Press / (or Click the divide button on the calculator)
  • Answer 0.88587014 ft/sec for the retract velocity
  • Do the same as above but omit the third and fourth steps for the extend velocity.
  • Answer 0.73207324 ft/sec for the extend velocity.
  • If SI was selected with AutoConv the answers would be 0.27001322 m/sec and 0.22313592 m/sec respectively.
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8. 250 SUS oil is flowing through a 1 in schedule 40 pipe at a flow rate of 189 liters per minute, what is the Reynolds number?

Equation: Image Solution: (AutoConv and US selected)
  • Type 189L/min <ENTER>
  • Type 1.049in (ID for a 1 inch schedule 40 pipe), Double Click Area
  • Press / (or Click the divide button on the calculator) 18.53477422 ft/sec appears in the display
  • Type 1.049in
  • Press * (or Click the multiply button on the calculator)
  • Type 250sus
  • Press / (or Click the divide button on the calculator).
  • Answer 2763.97321835. (NOTE: This number will be unitless if AutoConv has been selected)
    NOTE: If AutoConv is unselected, this answer will be 3.60196474 in*l/min*cSt. To get Reynolds number from this Type 1, Press F11 and the answer will be 2763.97321835.
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9. What is the velocity head of the above flow?

Equation: Image Solution: (AutoConv and SI selected)
  • Type 189L/min <ENTER>
  • Type 1.049in (ID for a 1 inch schedule 40 pipe), Double Click Area
  • Press / (or Click the divide button on the calculator) 5.64939918 m/sec appears in the display
  • Click x2 button, 31.91571113 m^2/sec^2 appears in the display.
  • Type 2, Press / (or Click the divide button on the calculator).
  • Click the g button 9.80665 m/sec^2 appears in the display.
  • Press / (or Click the divide button on the calculator).
  • Answer 1.62724840 m.
  • If US was selected with AutoConv the answer will be 5.33874148 ft.
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10. If the friction factor is 0.03, what is the head loss per 1ft of pipe?

Equation: Image Solution: (AutoConv and SI selected)
  • Type 189L/min <ENTER>
  • Type 1.049in (ID for a 1 inch schedule 40 pipe), Double Click Area
  • Press / (or Click the divide button on the calculator) 5.64939918 m/sec appears in the display
  • Click x2 button, 31.91571113 m^2/sec^2 appears in the display.
  • Type 2, Press / (or Click the divide button on the calculator).
  • Click the g button 9.80665 m/sec^2 appears in the display.
  • Press / (or Click the divide button on the calculator).
  • Answer 1.62724840 m. This is the velocity head.
  • Type 1ft <ENTER> (1 foot length of pipe)
  • Type 1.049in, / (or Click the divide button on the calculator). Press * ( or Click the multiply button).
  • Type 0.03, Press *, Answer 0.55844559 m.
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11. A pump has an overall efficiency of 90%. The maximum pressure that the pump will produce is 10.24 Mpa and the flow rate is 10 GPM, what size electric motor must be used to drive it in hp and kW?

Equation: Image Solution: (AutoConv and SI selected)
  • Type 10.24mpa <ENTER>
  • Type 10gpm, Press * (or Click the multiply button on the calculator)
  • Type 0.9, Press / (or Click the divide button on the calculator).
  • Answer 7178.26234596 N*m/sec.
  • Type hp, Press F11 function key .
  • Answer 9.62620837 hp.
  • Type kw, Press F11, Answer 7.17826235 kW.
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12. A 3 kW motor is turning at 150 RPM, what is the torque output in in-lbf and N-m?

Equation: Image Solution: (AutoConv and US selected)
  • Type 3kw <ENTER>
  • Type 150rpm, , Press / (or Click the divide button on the calculator).
  • Answer 140.86399427 lbf*ft.
  • Type n-m, Press F11 function key.
  • Answer 190.98593171 N*m
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13. How many gallons of water fall on a 10 acre field for a 1 inch rainfall?

Equation: Image Solution: (AutoConv and US selected)
  • Type 10acre <ENTER>
  • Type 1in, Press * (or Click the multiply button on the calculator).
  • Type gal, Press F11 function key.
  • Answer. 271542.85714286 gal.
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14. A small field is 350 feet wide by 500 feet long, if the pump used for irrigating the field will produce 25 GPM, how long must the field be watered to produce the equivalent of a 1 inch rainfall?

Equation: Image Solution: (AutoConv and US selected)
  • Type 350ft <ENTER>
  • Type 500ft, Press * (or Click the multiply button on the calculator).
  • Type 1in, Press * (or Click the multiply button on the calculator).
  • Type 25gpm, Press / (or Click the divide button on the calculator).
  • Answer; 261818.1818182 sec.
  • Type hr, Press F11 Answer 72.7272727 hr.
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15. How many acres are in the above lawn?

Equation: Image Solution: (AutoConv and US selected)
  • Type 350ft <ENTER>
  • Type 500ft, Press * (or Click the multiply button on the calculator).
  • Click the button beside the Convert button, this will bring up the Units Selector dialog pages. Select the Area page, then Click the Acre button, then OK.
  • Answer 4.01744720 Acre.
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16. A bicycle tire is 70 cm in diameter, how many revolutions are needed to go 1 mile?

Equation: Image Solution: (AutoConv and US selected)
  • Type 1mi <ENTER>
  • Type 70cm/rev <ENTER>
  • Click the p button.
  • Press * (or Click the multiply button on the calculator).
  • Press / (or Click the divide button on the calculator).
  • Answer 263453.19709915 deg.
  • Type rev then Press F11, Answer 731.81443639 rev.
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17. A tensile force of 500 lbf is placed on a 35 mmdiameter bar, what is the normal stress in Mpa?

Equation: Image Solution: (AutoConv and SI selected)
  • Type 500lbf <ENTER>
  • Type 35mm, Double Click Area
  • Press / (or Click the divide button on the calculator).
  • Answer 2311694.5568520 N/m^2.
  • Press mpa then F11, Answer 2.3116946 MPa.
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18. A steel shaft is subjected to a 175 N-m torque. The allowable shear stress is 30 ksi, what is the smallest diameter in inches for this shaft?

Equation: Image Solution: (AutoConv and SI selected)
  • Type 16 <ENTER>
  • Type 175n-m.
  • Press * (or Click the multiply button on the calculator).
  • Click p , Press / (or Click the divide button on the calculator).
  • Type 30ksi, Press / (or Click the divide button on the calculator).
  • Type 3 Double Click Image(the x root of y function) on the calculator.
  • Answer 0.0162726 m, Type in Press F11, Answer 0.6406521 in.
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19. What is the force on a gear tooth if 2 hp are being transmitted at 1000 RPM and the pitch diameter is 110 mm?

Equation: Image Solution: (AutoConv and US selected)
  • Type 2hp <ENTER>
  • Type 1000rpm, Press / (or Click the divide button on the calculator).
  • Type 2, Press * (or Click the multiply button on the calculator).
  • Type 110mm, Press / (or Click the divide button on the calculator).
  • Answer 58.2125120 lbf.
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20. A corn bin is 24 ft in diameter. If 5500 bu of corn are to be put in the bin, how deep will the corn be in ft?

Equation: Image Solution: (AutoConv and US selected)
  • Type 5.5x103bu or 5.5e3bu or 5500bu <ENTER>
  • Type 24ft, Double Click Area
  • Press / (or Click the divide button on the calculator).
  • Answer 15.1296846 ft.
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21. What is the volumetric displacement of a gear pump where the root diameter of the gears is 75 mm, the OD is 95 mm, and the width of the gears is 1.15 inches. Find VD in liters per minute.

Equation: Image Solution: (AutoConv and US selected)
  • Type 95mm, Double Click Area
  • Type 75mm, Double Click Area
  • Press - (or the subtract key on the calculator).
  • Type 1.15in, Press * (or Click the multiply button on the calculator).Answer 4.7599151 in^3.
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22. If this pump has a volumetric efficiency of 95% and the speed is 750 RPM, how much flow will be produced in GPM?

Equation: Image Solution: (AutoConv and US selected)
  • Type 95mm, Double Click Area
  • Type 75mm, Double Click Area
  • Press, - (or the subtract key on the calculator).
  • Type 1.15in, Press * (or Click the multiply button on the calculator).
  • Answer 4.7599151 in^3.
  • Click the cursor after the 3 in the answer, then Type /rev so that the display reads 4.7599151 in^3/rev, then <ENTER>.
  • Type 750rpm, Press * (or Click the multiply button on the calculator).
  • Type 0.95, Press / (or Click the divide button on the calculator).
  • Answer 62.6304618 in^3/sec
  • Type gpm, Press F11, Answer 16.2676524 GPM
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23. What is the pressure in psi and MPa on a diver in the ocean at a depth of 150 m.

The specific weight of sea water is Image
Equation: Image Solution: (AutoConv and SI selected)
  • Type 64lbf/ft^3 <ENTER>
  • Type 150m, Press * (or Click the multiply button on the calculator).
  • Answer 1508039.6529220 N/m^2.
  • Type psi, Press F11. Answer 218.7226597 psi.
  • Type mpa, Press F11. Answer 1.5080397 Mpa.
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24. A hydraulic pump has a maximum pressure rating of 1500 psi and a rated flow of 15.6 GPM. If a 220 V motor is to drive the pump, what is the approximate current that the motor will draw at full power?

Equations: Image Solution: (AutoConv and US selected)
  • Type 1500psi <ENTER>
  • Type 15.6gpm, Press * (or Click the multiply button on the calculator).
  • Answer 7507.50000000 lbf*ft/sec
  • Type 220v, Press / (or Click the divide button on the calculator).
  • Answer 46.26728749 A.
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