If a pump discharges 284 liters/min of water whose density is 985 kg/m3, find (a) the mass flow rate in kg /min, b) the total time to fill a cylindrical tank 3.05 m. in diameter and 3.05 m high.
a) Ah, the good old mass flow rate! Let's do some math, shall we? To find the mass flow rate, we need to multiply the volumetric flow rate (284 liters/min) by the density of water (985 kg/m³). So, grab your calculator and let's get to it!
Mass Flow Rate = Volumetric Flow Rate × Density
Mass Flow Rate = 284 liters/min × 985 kg/m³
Now, we need to convert liters to cubic meters, because they are like apples and oranges. There are 1000 liters in a cubic meter, so divide the volumetric flow rate by 1000.
Mass Flow Rate = (284 liters/min ÷ 1000) × 985 kg/m³
Simplify and calculate, my friend!
b) Now, let's move on to the total time it takes to fill the cylindrical tank. We'll need the volume of the tank and the mass flow rate we just calculated.
The volume of a cylinder is given by the formula:
Volume = π × (radius)² × height
Since the diameter of the tank is 3.05 m, the radius is half of that (1.525 m). The height is also 3.05 m. Now, let's crunch the numbers!
Volume = π × (1.525 m)² × 3.05 m
With the volume and mass flow rate, we can find the time it takes to fill the tank using this formula:
Time = Volume ÷ (Volumetric Flow Rate)
But since we've already calculated the mass flow rate, we can tweak this equation a bit:
Time = Volume ÷ (Mass Flow Rate ÷ Density)
Now, plug in the values and let the magic happen!
Time = [π × (1.525 m)² × 3.05 m] ÷ [(284 liters/min ÷ 1000) × 985 kg/m³]
And there you have it! You're just a few calculations away from the answers you seek. Enjoy the math-fueled ride!
To find the mass flow rate of water from the pump, we can use the formula:
Mass flow rate = Volume flow rate * Density
Given:
Volume flow rate = 284 liters/min
Density of water = 985 kg/m3
Step 1: Convert the volume flow rate to cubic meters per minute:
1 liter = 1/1000 cubic meters
284 liters/min = 284/1000 cubic meters/min = 0.284 cubic meters/min
Step 2: Calculate the mass flow rate:
Mass flow rate = 0.284 cubic meters/min * 985 kg/m3 = 279.44 kg/min
Therefore, the mass flow rate of water from the pump is 279.44 kg/min.
To find the total time to fill the cylindrical tank, we can use the formula:
Volume of cylinder = π * r2 * h
Given:
Diameter of the cylinder = 3.05 m
Radius (r) = Diameter/2 = 3.05/2 = 1.525 m
Height (h) = 3.05 m
Step 1: Calculate the volume of the cylindrical tank:
Volume of cylinder = π * (1.525)2 * 3.05 = 23.225 cubic meters
Step 2: Convert the volume flow rate to cubic meters per minute:
0.284 cubic meters/min
Step 3: Calculate the time to fill the cylindrical tank:
Time = Volume of cylinder / Volume flow rate
= 23.225 cubic meters / 0.284 cubic meters/min
= 81.74 minutes
Therefore, the total time to fill the cylindrical tank is approximately 81.74 minutes.
To find the mass flow rate of water discharged by the pump in kg/min, we need to multiply the volumetric flow rate (284 liters/min) by the density of water (985 kg/m^3). Here's how you can solve it step by step:
Step 1: Convert the volumetric flow rate to cubic meters per minute.
To do this, we need to convert liters to cubic meters since 1 liter is equal to 0.001 cubic meters.
284 liters/min * 0.001 m^3/liter = 0.284 m^3/min
Step 2: Calculate the mass flow rate using the density of water.
Mass flow rate (kg/min) = Volumetric flow rate (m^3/min) * Density (kg/m^3)
Mass flow rate = 0.284 m^3/min * 985 kg/m^3 = 279.34 kg/min
So, the mass flow rate of water discharged by the pump is 279.34 kg/min.
Next, to find the total time needed to fill the cylindrical tank, we'll use the volume of the tank and the mass flow rate.
Step 3: Calculate the volume of the cylindrical tank.
The volume of a cylinder can be calculated using the formula V = π * r^2 * h, where r is the radius and h is the height.
Given that the diameter of the tank is 3.05 m, the radius (r) will be half of that.
Radius (r) = 3.05 m / 2 = 1.525 m
Height (h) = 3.05 m
Volume (V) = π * (1.525 m)^2 * 3.05 m = 22.019 m^3
Step 4: Calculate the time using the mass flow rate and volume.
Time (minutes) = Volume (m^3) / Volumetric flow rate (m^3/min)
Time = 22.019 m^3 / 0.284 m^3/min ≈ 77.54 min
Therefore, it will take approximately 77.54 minutes to fill the cylindrical tank.
284L/min * 1m^3/1000L * 985kg/m^3 = 279.74 kg/min
π*(3.05/2)^2*3.05 m^3 / (284L/min * 1m^3/1000L) = 78.464 min