Tutorial Examples
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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: 
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
button 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
button 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: 
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: 
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: 
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: 
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: 
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: 
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: 
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: 
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: 
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: 
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: 
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: 
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: 
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: 
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 
(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: 
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: 
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: 
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: 
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 
Equation: 
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: 
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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