dimensional analysis

[studygives]

When filling a certain product, 400 liter drums are used. It takes 10 minutes to fill a drum. In this way, calculate (a) The volumetric flow of the pipe used to fill the drums. (b) The pipe diameter, in the SI, knowing that the flow velocity is 4 m / s. (c) Production, after 24 hours, disregarding the travel time of the drums.

 

[Deleted member 4993]

When filling a certain product, 400 liter drums are used. It takes 10 minutes to fill a drum. In this way, calculate (a) The volumetric flow of the pipe used to fill the drums. (b) The pipe diameter, in the SI, knowing that the flow velocity is 4 m / s. (c) Production, after 24 hours, disregarding the travel time of the drums.

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[Dr.Peterson]

When filling a certain product, 400 liter drums are used. It takes 10 minutes to fill a drum. In this way, calculate (a) The volumetric flow of the pipe used to fill the drums. (b) The pipe diameter, in the SI, knowing that the flow velocity is 4 m / s. (c) Production, after 24 hours, disregarding the travel time of the drums.

(a) is asking for something like liters per minute.

(b) might be thought of as asking, how big a pipe would hold, in a 4 meter length, the volume you need in one second. Or you could do it in several other ways.

(c) apparently wants the number of liters filled in 24 hours, assuming constant filling.

 

[HallsofIvy]

When filling a certain product, 400 liter drums are used. It takes 10 minutes to fill a drum. In this way, calculate (a) The volumetric flow of the pipe used to fill the drums. (b) The pipe diameter, in the SI, knowing that the flow velocity is 4 m / s. (c) Production, after 24 hours, disregarding the travel time of the drums.

(a) 400 liters in 10 minutes is, of course, 400/10= 40 liters per minute or 40/60= 2/3 liters per s. Since the flow velocity is 4 m/s, 4 meters of the pipe contains 2/3 liters. If the pipe has radius r meters, the cross section area of the pipe is \(\displaystyle \pi r^2\) so the volume of 4 meters of that pipe is \(\displaystyle 4\pi r^2= 2/3\).

Since the the flow is 40 liters per minute, in 24 hours= 24(60)(40)= 57600 liters.