if a pump discharges 75 gpm of water whose specific weight is 61.5 lb/ft^3(g=31.95fps^2). find a) the mass flow rate in lb/min, and b) and total time required to fill a vertical cylinder tank 10ft in diameter and 12ft high.
(1) There are 7.48 ft^3 in a gallon. Therefore the volume flow rate can be expressed as 75 gallon/min/7.48 gal/ft^3 = 10.03 ft^3/min
Multiply that by the density of water, 62.4 lbm/ft^3, and you get 626 lbm/min.
(lbm stands for pounds mass; the preferred mass unit in the British system is slugs)
(2) Time = Volume/Flow rate
= (pi/4)*D^2*L/10.03 ft^3/min
= 94.0 minutes
is there really a 7.48ft^3 in a gallon?...
isn't it 0.133681?
a) To find the mass flow rate in lb/min, we can use the equation:
Mass flow rate = Volume flow rate * Specific weight of water
The specific weight of water is given as 61.5 lb/ft^3, and the volume flow rate is given as 75 gpm. We need to convert gpm to ft^3/min.
Since 1 gallon = 0.1337 ft^3, we can calculate the volume flow rate as:
Volume flow rate = 75 gpm * (1 ft^3/0.1337 gal) = 560.05 ft^3/min.
Now we can calculate the mass flow rate:
Mass flow rate = 560.05 ft^3/min * 61.5 lb/ft^3 = 34,404.075 lb/min.
b) To find the total time required to fill a vertical cylinder tank, we need to calculate the volume of the tank and divide it by the volume flow rate.
The formula to calculate the volume of a cylinder is:
Volume = π * r^2 * h
Given the diameter of the tank is 10ft, the radius (r) would be half of that, which is 5ft. The height (h) is given as 12ft.
So, Volume = π * (5ft)^2 * 12ft = 942.48 ft^3
Now, we can calculate the time required:
Time = Volume / Volume flow rate
Time = 942.48 ft^3 / 560.05 ft^3/min = 1.68 min
Therefore, the total time required to fill the vertical cylinder tank is approximately 1.68 minutes. Just imagine all the water park jokes you can make while waiting for the tank to fill!
To find the mass flow rate in lb/min, we need to convert the volumetric flow rate (gpm) to mass flow rate (lb/min). We can use the equation:
Mass flow rate = Volumetric flow rate × Specific weight
a) Mass flow rate in lb/min:
Given, Volumetric flow rate = 75 gpm
Specific weight of water = 61.5 lb/ft^3
First, we need to convert gpm to ft^3/min:
1 gpm = 7.481 ft^3/min (approximately)
Volumetric flow rate = 75 gpm = 75 × 7.481 ft^3/min
Now, we can calculate the mass flow rate:
Mass flow rate = Volumetric flow rate × Specific weight
Mass flow rate = (75 × 7.481) ft^3/min × 61.5 lb/ft^3
Simplifying the equation:
Mass flow rate ≈ 56,076.375 lb/min
Therefore, the mass flow rate is approximately 56,076.375 lb/min.
b) To find the total time required to fill a vertical cylinder tank, we need to consider the volume of the tank and the volumetric flow rate of the pump.
Given, Diameter of the tank = 10 ft
Height of the tank = 12 ft
First, let's find the volume of the vertical cylinder tank:
Volume = πr^2h
Where r is the radius of the tank (diameter/2).
Radius (r) = 10 ft/2 = 5 ft
Volume = π × (5 ft)^2 × 12 ft
Volume ≈ 942.48 ft^3 (approximately)
Now, we can calculate the time using the volumetric flow rate:
Time = Volume / Volumetric flow rate
Volumetric flow rate = 75 gpm = 75 × 7.481 ft^3/min (from previous calculation)
Time = 942.48 ft^3 / (75 × 7.481) ft^3/min
Simplifying the equation:
Time ≈ 2.5286 min
Therefore, the total time required to fill the vertical cylinder tank is approximately 2.5286 minutes.