# Storm Water Drain Inlet Calculations Spreadsheet

Introduction

Design of storm water drain inlets is basically determining the size opening needed to handle the design peak storm water runoff rate, for the particular type of inlet opening.  The links above also have spreadsheets for calculating the peak storm water runoff rate with the Rational Method equation.

Types of Pavement Drain Inlets

The types of pavement drain inlets in common use include curb inlets, gutter inlets and combination inlets.  A curb inlet is just an opening in the curb as shown in the image at the left.  A combination inlet has both a curb opening and a grate opening in the bottom of the gutter as shown in the image at the right.  Gutter inlets typically have a grate over the opening, while curb inlets are typically open without a grate, as shown in the pictures.  A sketch of a depressed gutter inlet is shown at the bottom left.

Curb Inlet Image Credit: Lone Star Manhole and Structures

Combination Inlet Image Credit: Robert Lawton – Wikimedia Commons

Depressed Gutter Inlet Image Credit:  H. H. Bengtson

The Weir Model for Sizing Storm Water Drain Inlets

The openings for storm water drains can be modeled as a weir if the opening isn’t completely submerged at the design storm water runoff flow rate.  For a curb opening this would be the case if the depth of storm water at the opening is less than the height of the opening.  For a gutter opening it would occur if the design flow rate of storm water runoff enters the grate around the edges, without completely submerging the opening.

The equation used to size storm drains with unsubmerged openings is theC sharp crested weir equation:  Q = CwLd1.5, where:

• Q = the design storm water runoff rate that must flow through the inlet in cfs for U.S. or m3/s for S.I. units.
• Cw = a weir coefficient, which is a dimensionless constant.  Typical values are 2.3 for U.S. units and 1.27 for S.I. units.
• L = the length of the curb opening (or the length of the the gutter opening in the direction of the storm water flow), in ft for U.S. or m for S.I. units.
• d = the depth of storm water above the bottom of the curb opening or its depth above the gutter inlet opening in ft for U.S. or m for S.I. units.

The Orifice Model for Sizing Storm Water Drain Inlets

The storm water drain opening can be modeled as an orifice if it will be completely submerged at design flow of storm water runoff.  This would be the case for a curb opening if the water depth is more than the height of the curb opening at design storm water flow.  A gutter opening could be modeled as a weir if the gutter opening is completely submerged at the design storm water runoff rate.  The equation used for sizing storm water inlets with the orifice model is:

Q = Co A(2gde)1/2 ,  where:

• Q = the design storm water runoff rate that must flow through the inlet in cfs for U.S. or m3/s for S.I. units.
• Co = the orifice coefficient, which is dimensionless.  The value typically used for storm water inlet design is 0.67.
• A = the area of the inlet opening in ft2 for U.S. or m2 for S.I. units.
• g = the acceleration due to gravity (32.2 ft/sec2 for U.S. or 9.82 m/s2 for S.I units).
• de = the height of storm water above the centroid of the opening in ft for U.S. or m for S.I. units.

Note that de = d – h/2, for a curb opening, where d is the depth of storm water above the bottom of the opening and h is the height of the curb opening.  For a gutter opening,  de = d, where d is the height of storm water above the gutter opening at design storm water flow.

An Excel Spreadsheet as a Storm Water Drain Inlet Design Calculator

The Excel spreadsheet template shown below can be used to calculate the required size of a curb inlet for storm water drainage, based on specified information about the design storm water runoff rate, height of the curb opening, and the height of the storm water above the bottom of the opening.  Why bother to make these calculations by hand?  This Excel spreadsheet and others with similar calculations for a gutter opening are available in either U.S. or S.I. units at a very low cost in our spreadsheet store.

References:

1. McCuen, Richard H., Hydrologic Analysis and Design, 2nd Ed, Upper Saddle River, NJ, 1998.

2. ASCE. 1992. Design and Construction of Urban Stormwater Management Systems. The Urban Water Resources Research Council of the American Society of Civil Engineers (ASCE) and the Water Environment Federation. American Society of Civil Engineers, New York, NY.

3. Texas Department of Transportation/Online Hydraulic Design Manual/Storm Drain Inlets.

# Heat Exchanger Thermal Design Calculations Spreadsheet

## The Basic Equation for a Heat Exchanger Thermal Design Calculations Spreadsheet

The basic heat exchanger design equation is:  Q = U A ΔTlm,    where:

• Q = the rate of heat transfer between the two fluids in the heat exchanger in But/hr (kJ/hr for S.I. units)
• U is the overall heat transfer coefficient in Btu/hr-ft2oF  (kJ/hr-m2-K for S.I. units)
• A is the heat transfer surface area in ft2 (m2 for S.I. units)
• ΔTlm is the log mean temperature difference in oF,  (K for S.I units)  calculated from the inlet and outlet temperatures of both fluids.

For a heat exchanger thermal design calculations spreadsheet, the heat exchanger equation can be used to calculate the required heat exchanger area for known or estimated values of the other three parameters, Q, U, and ΔTlm.  Each of those parameters will be discussed briefly in the next three sections.

## The Log Mean Temperature Difference, ΔTlm , for a Heat Exchanger Design Spreadsheet

The driving force for a heat transfer process is always a temperature difference. For heat exchangers, there are always two fluids involved, and the temperatures of both are changing as they pass through the heat exchanger.  Thus some type of average temperature difference is needed.  Many heat transfer textbooks (e.g. ref #1 below) show that the log mean temperature difference is the appropriate average temperature difference to use for heat exchanger design calculations.  The definition of the log mean temperature difference is shown in the figure above.  The meanings of the four temperatures in the log mean temperature difference equation are rather self explanatory as shown in the diagram of a counterflow double pipe heat exchanger at the right.

## The Heat Transfer Rate, Q, for a Heat Exchanger Thermal Design Calculations Spreadsheet

In order to use the heat exchanger design equation to calculate a required heat transfer area,  a value is needed for the heat transfer rate, Q.  This rate of heat flow can be calculated if the flow rate of one of the fluids is known along with its specific heat and the required temperature change for that fluid. The equation to be used is shown below for both the hot fluid and the cold fluid:

Q = mH CpH (THin – THout) = mC CpC (TCout – TCin), where

• mH is the mass flow rate of the hot fluid in slugs/hr (kg/hr for S.I. units).
• CpH is the specific heat of the hot fluid in Btu/slug-oF (kJ/kg-K for S.I. units).
• mC is the mass flow rate of cold fluid in slugs/hr (kg/hr for S.I. units).
• CpC is the specific heat of the cold fluid in Btu/slug-oF (kJ/kg-K for S.I. units).
• The temperatures (THin, THout, TCout, & TCin) are the hot and cold fluid temperatures going in and out of the heat exchanger, as shown in the diagram above.  They should be in oF for U.S. or K for S.I. units.

The heat transfer rate, Q, can be calculated in a preliminary heat exchanger design spreadsheet if the flow rate, heat capacity and temperature change are known for either the hot fluid or the cold fluid. Then one unknown parameter can be calculated for the other fluid.  (e.g. the flow rate, the inlet temperature, or the outlet temperature.)

## The Overall Heat Transfer Coefficient, U, for a Heat Exchanger Design Spreadsheet

The overall heat transfer coefficient, U, depends on the convection coefficient inside the pipe or tube, the convection coefficient on the outside of the pipe or tube, and the thermal conductivity of the pipe wall.  See the article, Forced Convection Heat Transfer Coefficient Calculations, for information about calculating the heat transfer coefficients and click here to visit our spreadsheet store, for spreadsheets to calculate the inside and outside convection coefficients and to calculate the overall heat transfer coefficient.

## A Heat Exchanger Thermal Design Calculations Spreadsheet

The screenshot below shows a heat exchanger thermal design calculations spreadsheet that can be used to carry out thermal design of a double pipe heat exchanger.  The image shows only the beginning of the calculations.  The rest of the spreadsheet will calculate the length of pipe needed, the length of each pass for a selected number of 180 degree bends, and the pressure drop through the inside of the pipe.  Why bother to make these calculations by hand?  This Excel spreadsheet is available in either U.S. or S.I. units at a very low cost at in our spreadsheet store.

References

1. Kuppan, T., Heat Exchanger Design Handbook, CRC Press, 2000.

2. Kakac, S. and Liu, H., Heat Exchangers: Selection, Rating and Thermal Design, CRC Press, 2002.

3. Bengtson, H., Fundamentals of Heat Exchangers, an online, continuing education course for PDH credit.

4. Bengtson, H., Thermal Design of a Double Pipe Heat Exchanger, and online blog article.