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
To calculate the maximum water velocity at the outlet hole, we can use the equation:
V = sqrt(2 * g * H)
Where:
V is the flow velocity
g is the acceleration due to gravity (32.2 ft/s^2)
H is the height of the water level above the hole (41.5 inches)
First, let's convert the height H from inches to feet by dividing it by 12:
H = 41.5 / 12 = 3.458 feet
Now, let's substitute the values into the equation:
V = sqrt(2 * 32.2 * 3.458)
V ≈ 9.86 ft/s
So, the maximum water velocity you can expect at the outlet hole is approximately 9.86 ft/s.
To calculate the maximum flow rate (Q) in gallons per minute (gal/min), we need to know the area of the hole and convert the volume flow rate from cubic feet per second (ft^3/s) to gallons per minute (gal/min).
The area of the hole can be determined using the formula for the area of a circle:
A = π * r^2
Where:
A is the area of the hole
π is a constant (approximately 3.14159)
r is the radius of the hole, which is half of the diameter (1 inch / 2 = 0.5 inches)
Now, let's convert the radius from inches to feet:
r = 0.5 / 12 = 0.04167 feet
Substituting the values into the equation:
A = 3.14159 * (0.04167)^2
A ≈ 0.002146 ft^2
Next, we can calculate the volume flow rate (Q) using the equation:
Q = A * V
Substituting the values into the equation:
Q = 0.002146 * 9.86
Q ≈ 0.02114 ft^3/s
Finally, to convert the volume flow rate from cubic feet per second (ft^3/s) to gallons per minute (gal/min), we need to multiply by an appropriate conversion factor:
1 ft^3/s = 448.831 gal/min
So, the maximum flow rate you can expect is approximately:
Q ≈ 0.02114 * 448.831
Q ≈ 9.50 gal/min
Therefore, the maximum flow rate you can expect from your system is approximately 9.50 gallons per minute (gal/min).