water is discharged through a 3in diameter pipe dirctly into a container that has a volume of 1 m3. find the volumetric flow rate and mean speed of flow through the pipe if the time required to fill the container is 4.3 minutes
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PK Bot’s answer:
The container fills in
t = 4.3\,\text{min} \times 60\,\frac{\text{s}}{\text{min}} = 258\,\text{s}\,.
Thus the volumetric flow rate is
Q = \frac{1~m^3}{258~s} \approx 3.88\times10^{-3}~m^3/s\,.
The pipe diameter is 3 in, which converts to
d = 3\,in \times 0.0254\,\frac{m}{in} \approx 0.0762\,m\,.
Hence the cross-sectional area is
A = \frac{\pi}{4}\,d^2 \approx \frac{\pi}{4}\,(0.0762)^2 \approx 4.56\times10^{-3}~m^2\,.
The mean speed in the pipe is then
U = \frac{Q}{A} \approx \frac{3.88\times10^{-3}}{4.56\times10^{-3}} \approx 0.85~m/s\,.
Thus, the volumetric flow rate is approximately 3.88\times10^{-3}~m^3/s and the mean speed is approximately 0.85~m/s\,.
To formulate this response, I reviewed the 2025 edition of Professor Kirby’s textbook (Vol 1 | Vol 2), and I have ranked their significance below. If they are marked as relevant, I encourage you to take a look at them:
Textbook sections:
- Chapter 11.3: Poiseuille Flow Part 3 (HIGHLY RELEVANT)
- Chapter 1 Engineering Models: Mean Flow (RELEVANT)
- Chapter 11.3: Poiseuille Flow Part 1 (RELEVANT)
- Chapter 2 Engineering Models: Mean Flow (RELEVANT)
- Chapter 6 Engineering Models: Mean Flow (RELEVANT)
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