Flow from a Tank at Constant Height

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This Demonstration calculates and displays the volumetric and mass flow rates of a liquid maintained at a constant height in a tank as a function of the liquid's height and density , the drain pipe's diameter and the discharge (orifice) coefficient . It also plots the volumetric flow rate curve as a function of the liquid's height for the chosen drain diameter and discharge coefficient values and displays a schematic diagram of the system.

Contributed by: Mark D. Normand, Maria G. Corradini, and Micha Peleg (March 2011)
Open content licensed under CC BY-NC-SA



Snapshot 1: water flow from a narrow drain

Snapshot 2: oil flow from a wide drain

Snapshot 3: concentrated sugar syrup flow from a narrow drain

This Demonstration depicts the flow from a tank where the liquid is maintained at a constant height. It shows that the liquid's flow rate is proportional to the square root of its height. The program calculates the volumetric flow rate, , using a slightly modified Bernoulli equation , where is the gravitational constant (9.81 ), is the liquid's height in the tank (m), is the discharge (orifice) coefficient (dimensionless), and the drain diameter (cm). The corresponding mass flow rate (kg/s) is calculated by multiplying the volumetric flow rate, , by the liquid's density, ().


R. L. Earle and M. D. Earle, Unit Operations in Food Processing, NZIFST, Inc., 1983.

V. L. Streeter, E. B. Wylie, and K. W. Bedford, Fluid Mechanics, 9th ed., Boston: WCB/McGraw-Hill, 1998.

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