Roman Bath Water Balance ( Novel example of the hydrologic balance)

A water balance is an estimate of the conservation of water for an area of interest. The balance is defined by this equation: water in – water out = change in storage. Water balances are performed to evaluate the impact of construction on runoff, to assess how groundwater usage might impact the water table level and in many other assessments dealing with water quantity. As a novel example you will calculate a water balance for a Roman Bath. The ancient Romans loved their baths. In this exercise, you will calculate how much water per day had to be added to a bath to keep it filled at a constant water level in consideration of leakage and evaporation losses (i.e., water in = water out+ or – change in storage). We will assume it takes a whole day to fill the bath. The bath in question is a hot bath in the ancient Roman city of Ostia Antica some 30 miles from Rome. Watch the video to learn more about the baths in the time of ancient Rome and for some needed measurements (Copy the depth of water, the width of the bath and the length of the bath). You will use these and the information below.

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Video with Captioning

Recall the general equation for a water balance is volume in – volume out = change in volume.  In this example the equation can be expressed as flow rate in – flow rate out  = net fill rate. Given the net fill rate and volume of the bath one can calculate how long it would take to fill the bath = volume of bath/net fill rate.  Given the net fill rate you can also calculate how high the water would be in the bath for a given time = net fill rate * time/width*length of the bath.

Your objective is to determine: (1) how long would it take to fill the bath ( to the hieght given in the video) assuming an input fill rate of 24″/day and output losses of 7.2 inches/day by evaporation and 5.4 inches/day due to leakage.

Water Balance Calculation

  • Volume of Bath (cubic feet) =Depth*Length*Width
  • Fill rate =(width * length of the bath * 24) /12 ( CF/day)
  • Leak Rate = (width* length of the bath* 7.2)/12 (CF/day)
  • Leak Rate = (width* length of the bath* 5.4)/12 (CF/day)
  • Total rate of loss (CF/day) =Leak rate + evapoartion rate
  • Net rate of filling = rate of filling - total loss rate. This is our water balance.
  • Number of days = volume of the bath/net rate of filling
  • height = net rate of filling* time /(width*length)
  • This field is for validation purposes and should be left unchanged.

Narration:
Dr. Gary Robbins, Dept. of Natural Resources and the Environment, U. Connecticut, Storrs, CT
Dr. Darius Arya, Director, American Institute for Roman Culture, Rome, Italy
Music:
Michael Levy, “Ode to Ancient Rome”, https://ancientlyre.com/ancient-roman-themed-albums
Video:
Gary Robbins and Michael Gemmell