BIZOMAT MAKEOS · Hydraulics
Sump or Pit Pump-Out Plan (Simpson Section Area, Volume, Time)
How much water is in this pit or sump of irregular cross-section, and how long will my pump take to empty it with water still running in?
Pump-out plan for a pit, trench or sump of uniform length with an irregular cross-section: the section area by Simpson’s rule from depths measured at equal spacings across it (as the Simpson’s rule area tool), the volume over the length, the net pumping rate after inflow, and the time to empty, against the time you have.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Spacing between depth readings | mm | Equal spacing between the depth readings across the pit. |
| Number of spaces (even) | Number of spaces between readings (must be even). | |
| Depths at each reading, d₀ … d₁₀ (only d₀ to d_N are used) | ||
| d0 | mm | Water depth at the first reading. |
| d1 | mm | Depth at reading 1. |
| d2 | mm | Depth at reading 2. |
| d3 | mm | Depth at reading 3. |
| d4 | mm | Depth at reading 4. |
| d5 | mm | Depth at reading 5. |
| d6 | mm | Depth at reading 6. |
| d7 | mm | Depth at reading 7. |
| d8 | mm | Depth at reading 8. |
| d9 | mm | Depth at reading 9. |
| d10 | mm | Depth at reading 10. |
| Pumping | ||
| Length of the pit | mm | Length of the pit along which the section is uniform. |
| Pump flow | L/min | Flow the pump delivers at the pumping head. |
| Inflow while pumping | L/min | Water still entering while pumping. |
| Time available | min | Time you have to empty it. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Spacing between depth readings
- What it is
- The equal horizontal spacing between neighbouring depth readings taken across the width of the pit.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 500 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Section area, volume and time to empty rise in direct proportion to the spacing.
- Get it right
- All spaces must be equal for Simpson’s rule; measure the readings at a fixed interval from one edge.
What this means: Number of spaces (even)
- What it is
- The number of equal spaces between depth readings across the pit, which is one less than the number of readings.
- Units and format
- Enter a plain number with no unit. The form accepts 2 to 10. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It must be even for Simpson’s rule; readings beyond d_N are ignored.
Depths at each reading, d₀ … d₁₀ (only d₀ to d_N are used)
What this means: d0
- What it is
- The water depth at the first reading, at one edge of the section where the spacing starts.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- This is often zero at the water’s edge; measure vertically from the water surface.
What this means: d1
- What it is
- The water depth at the second reading, one spacing in from the first; Simpson’s rule weights it by 4.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 800 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure vertically from the water surface to the floor at this point.
What this means: d2
- What it is
- The water depth at the third reading, two spacings from the first edge; weighted by 2 unless it is the last reading.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1200 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure vertically at exactly two spacings from the first reading.
What this means: d3
- What it is
- The water depth at the fourth reading, three spacings from the first edge; weighted by 4.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1400 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Used only when the number of spaces is at least 4.
What this means: d4
- What it is
- The water depth at the fifth reading, four spacings from the first edge; weighted by 2 unless it is the last reading.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1500 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure vertically from the water surface at four spacings from the edge.
What this means: d5
- What it is
- The water depth at the sixth reading, five spacings from the first edge; weighted by 4 when used.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1400 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Used only when the number of spaces is at least 6.
What this means: d6
- What it is
- The water depth at the seventh reading, six spacings from the first edge; weighted by 2 unless it is the last reading.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1200 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Used only when the number of spaces is at least 6.
What this means: d7
- What it is
- The water depth at the eighth reading, seven spacings from the first edge; weighted by 4 when used.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 800 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Used only when the number of spaces is at least 8.
What this means: d8
- What it is
- The water depth at the ninth reading, eight spacings from the first edge; weighted by 2 unless it is the last reading.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Used only when the number of spaces is at least 8; with 8 spaces it is the far edge.
What this means: d9
- What it is
- The water depth at the tenth reading, nine spacings from the first edge, used only with 10 spaces and then weighted by 4.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Ignored unless the number of spaces is 10.
What this means: d10
- What it is
- The water depth at the eleventh reading, the far edge of a section divided into 10 spaces.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Ignored unless the number of spaces is 10.
Pumping
What this means: Length of the pit
- What it is
- The length of the pit at right angles to the measured section, over which that cross-section stays the same.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Volume and time to empty rise in direct proportion to length.
- Get it right
- If the section changes along the pit, split it into lengths and run each one separately.
What this means: Pump flow
- What it is
- The flow the pump actually delivers at the lift from the pit floor to the discharge point, read from its pump curve.
- Units and format
- Enter a number in L/min: litres per minute. The form accepts 0.000001 L/min to 10000000 L/min. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 600 L/min as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger pump flow raises the net pumping rate and shortens the time to empty.
- Get it right
- Read the flow at the full lift and hose losses, not the open-flow figure on the label.
What this means: Inflow while pumping
- What it is
- The rate at which water keeps entering the pit while it is being pumped, from seepage, drains or rain.
- Units and format
- Enter a number in L/min: litres per minute. The form accepts 0 L/min to 10000000 L/min. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 L/min as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- It is subtracted from the pump flow, so more inflow lengthens the time to empty.
- Get it right
- Estimate it by timing the rise of water with the pump off; it must be less than the pump flow.
What this means: Time available
- What it is
- The time you have available to empty the pit, set by the work programme or the next inflow event.
- Units and format
- Enter a number in min: minutes. The form accepts 0.000001 min to 1000000 min. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60 min as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter minutes, not hours.
Method and formulas
- Area = (spacing ÷ 3)(d₀ + 4d₁ + 2d₂ + … + 4d_(N−1) + d_N) (as the Simpson’s rule area tool).
- Volume = section area × length.
- Time = volume ÷ (pump flow − inflow).
- Example: the section is 4.2333 m², holding 25,400 L; at a net 500 L/min it takes 50.8 min.
Limitations
- Uniform section along the length; irregular pits need several sections averaged.
- Pump flow taken as constant although head rises as the level falls.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Plan dewatering of a machine pit or trench
- Estimate a sump volume from soundings
- Size a pump for a pump-out time
Who it is for
- Maintenance supervisors
- Plant engineers
- Site engineers
What you get
- Section area by Simpson’s rule
- Volume of water
- Net pumping rate and time to empty
Interpreting the result
- Inflow eats directly into pumping: a pump only slightly larger than the inflow never empties the pit.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 67–68. Topic reference; no source tables or recommended settings are reproduced.
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Open the Sump or Pit Pump-Out Plan (Simpson Section Area, Volume, Time) calculator