oil flows through a 4.0 cm i.d. pipe at an average speed of 2.5 m/s. find the flow in m3/s and cm3/s
cm^3/s = cm^2 * cm/s
so, your volume is
4π cm^2/s * 250 cm/s = 1000π cm^3/s
to get m^3/s, just multiply that by (1m/100cm)^3 or π/1000 m^3/s
Well, well, well, looks like our pipe is getting oily! Let's calculate the flow rate, shall we?
First, we need to find the cross-sectional area of the pipe. The inner diameter (i.d.) given is 4.0 cm. Now, I have an insider tip for you: the area of a circle can be calculated using the formula A = π*r^2.
To find the radius (r), we divide the diameter by 2. So, the radius is 4.0 cm / 2 = 2.0 cm.
Now we can calculate the area: A = π * (2.0 cm)^2.
But hold your horses, my friend! We need to convert from cm to meters to keep our units consistent. Now, there are 100 centimeters in a meter, so 2.0 cm is equal to 2.0 / 100 = 0.02 m.
Finally, plugging in the numbers: A = π * (0.02 m)^2.
Now, let's calculate the flow rate in cubic meters per second. The flow rate (Q) can be calculated using the formula Q = A * v, where v is the average velocity.
So, Q = (π * (0.02 m)^2) * 2.5 m/s.
Calculating this gives us the flow rate in cubic meters per second. For the final touch, we can also find the flow rate in cubic centimeters per second by converting the volume.
Remember that 1 m^3 is equal to 1,000,000 cm^3. So, we can multiply the flow rate in cubic meters per second by 1,000,000 to get the flow rate in cubic centimeters per second.
Voilà! Now you have the flow rate in both m^3/s and cm^3/s.
To find the flow rate in cubic meters per second (m^3/s), we need to first calculate the cross-sectional area of the pipe.
The inner diameter (i.d.) of the pipe is given as 4.0 cm. We can find the radius by dividing the diameter by 2:
Radius = 4.0 cm / 2 = 2.0 cm = 0.02 m
The cross-sectional area of a pipe can be calculated using the formula:
Area = π * (radius)^2
Area = π * (0.02 m)^2
Area ≈ 0.001256 m^2
Now, we can find the flow rate in cubic meters per second (m^3/s) by multiplying the cross-sectional area by the average speed:
Flow rate = Area * Speed
Flow rate = 0.001256 m^2 * 2.5 m/s
Flow rate ≈ 0.00314 m^3/s
To find the flow rate in cubic centimeters per second (cm^3/s), we need to convert the flow rate from cubic meters to cubic centimeters.
1 m^3 = 1,000,000 cm^3
So, the flow rate in cm^3/s is:
Flow rate = 0.00314 m^3/s * 1,000,000 cm^3/m^3
Flow rate ≈ 3140 cm^3/s
To calculate the flow rate of oil, we need to use the equation:
Flow rate = Area × Velocity
First, we need to calculate the cross-sectional area of the pipe. The cross-sectional area of a pipe can be calculated using the formula:
Area = π × (Radius)²
Given that the inner diameter (i.d.) of the pipe is 4.0 cm, we can find the radius (r) by dividing the diameter by 2:
Radius = i.d. / 2 = 4.0 cm / 2 = 2.0 cm = 0.02 m
Now, we can calculate the area:
Area = π × (0.02 m)² ≈ 0.00125663706 m²
Next, we can use the given average velocity of 2.5 m/s to calculate the flow rate in cubic meters per second (m³/s):
Flow rate = Area × Velocity = 0.00125663706 m² × 2.5 m/s ≈ 0.00314159265 m³/s
To convert m³/s to cm³/s, we need to multiply by 1,000,000 (since 1 m³ = 1,000,000 cm³):
Flow rate = 0.00314159265 m³/s × 1,000,000 ≈ 3141.59265 cm³/s
Therefore, the flow rate of oil is approximately 0.0031 m³/s and 3141.59 cm³/s.