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You want to water your garden with rainwater, and you place a 55 gal drum at the bottom of the downspout of your house gutter system to collect the water. The drum is 42" tall and you cut a 1 inch diameter hole at the lowest point of the side of the drum to install your outlet valve. What is the maximum water velocity you can expect to get out of your system. What is the max flow rate (gal/min) you can expect?

The flow vlocity through the hole is
V = sqrt (2 g H),
where H is the height of the water level above the hole. Measured to the cetner of the hole that would have a maximum value of 41.5 inches.
The volume flow rate through the hole
Q = A V,
where A is the area of the hole. Make sure you sure consistent units when using the equations. I suggest using H in feet, g = 32.2 ft/s^2, V in ft/s and Q in ft^3/s. Then convert cubic feet to gallons.

all that my teacher gave me was V=(2gh)^1/2

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