2. If a pump discharges 284 liters per minute of water whose density is 985 kg/m3
. Find (a) mass
flow rate in kg/min; (b) the total time required to fill a vertical cylindrical tank 3.05 m in
diameter, and 305 m high. Note: m = Q x ρ, where m= mass, Q=volume flow rate, ρ= density.
Volume of a cylinder is (π/4)(D2
)(h).
a) Mass flow rate in kg/min = 284 liters/min x 985 kg/m3 = 279.66 kg/min
b) Total time required to fill a vertical cylindrical tank = (Volume of tank)/(Mass flow rate)
= [(π/4)(3.05 m)2(305 m)]/(279.66 kg/min) = 8.45 minutes
To find the mass flow rate in kg/min, we can use the formula m = Q x ρ, where m is the mass, Q is the volume flow rate, and ρ is the density.
Given:
Volume flow rate, Q = 284 liters/min
Density, ρ = 985 kg/m3
First, we need to convert the volume flow rate from liters/min to m3/min:
1 liter = 0.001 m3
284 liters = 0.284 m3
Therefore, the volume flow rate in m3/min is 0.284 m3/min.
Now, we can calculate the mass flow rate:
m = Q x ρ
m = 0.284 m3/min x 985 kg/m3
m = 279.74 kg/min
So, the mass flow rate is 279.74 kg/min.
To find the total time required to fill a vertical cylindrical tank, we can use the formula for the volume of a cylinder: V = (π/4)(D2)(h), where V is the volume, D is the diameter, and h is the height.
Given:
Diameter, D = 3.05 m
Height, h = 305 m
Let's calculate the volume of the cylindrical tank:
V = (π/4)(D2)(h)
V = (3.14/4)(3.05 m)2(305 m)
V = 2251.97 m3
Since we know the volume flow rate is 0.284 m3/min, we can find the time required to fill the tank:
Time = V / Q
Time = 2251.97 m3 / 0.284 m3/min
Time = 7931.50 min
So, the total time required to fill the vertical cylindrical tank is approximately 7931.50 minutes.
To find the mass flow rate and the total time required to fill the cylindrical tank, we need to follow these steps:
(a) Calculate the mass flow rate:
Mass flow rate (m) = Volume flow rate (Q) x Density (ρ)
Given:
Q = 284 liters/min
ρ = 985 kg/m³
Note that the units need to be consistent, so we'll need to convert liters to cubic meters and minutes to seconds.
1 liter = 0.001 cubic meters
1 minute = 60 seconds
Substituting the values, we get:
Q = 284 liters/min x 0.001 cubic meters/liter x 1 min/60 seconds
= 0.00473 cubic meters/second
Now we can calculate the mass flow rate:
m = Q x ρ
= 0.00473 cubic meters/second x 985 kg/m³
= 4.65955 kg/second
To convert kg/second to kg/minute, we multiply by 60:
m = 4.65955 kg/second x 60 seconds/minute
= 279.573 kg/minute
Therefore, the mass flow rate is 279.573 kg/minute.
(b) Calculate the total time required to fill the cylindrical tank:
To calculate the total time, we need to find the volume of the tank and divide it by the volume flow rate.
Given:
Diameter (D) = 3.05 m
Height (h) = 305 m
Volume of a cylinder = (π/4)(D²)(h)
= (3.14159/4)(3.05²)(305)
= 8769.45765 cubic meters
Now divide the volume of the tank by the volume flow rate:
Time = Volume / Volume flow rate
= 8769.45765 cubic meters / 0.00473 cubic meters/second
≈ 1853613.83 seconds
Since we need the time in minutes, we divide by 60:
Time = 1853613.83 seconds / 60 seconds/minute
≈ 30893.5638 minutes
Therefore, the total time required to fill the cylindrical tank is approximately 30893.5638 minutes.