# Frame rate of a video: Calculating velocity of liquid

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1. Feb 7, 2015

### Fizz1cks

1. The problem statement, all variables and given/known data

The problem I have is not actually so much a physics problem but more of a logical problem. When we look at rulers and any kind of measuring tools, we start from zero. We count the number of intervals instead of the divisions. Suppose we have a video with 7 frames per second. This means it will take 1 second for it to play 7 frames. So, essentially, 1 frame should take 1/7 seconds. However, when we use any kind of a video editing tool, it starts with the first frame. Will that mean we have to suppose the first frame to be at time zero? It that's the case, then it will need eight frames instead of seven frames for the total time to add up to 1 second. For seven frames to take 1 second, the first frame has to be a blank frame. Although tons of videos on youtube have black/blank frames in the first frame, I think its more to do with the editing, as I also found tons of videos without the blank frames. So, the first frame starts at 0 seconds, instead of 1/7 seconds... it takes 1/7 seconds to move from frame 1 to frame 2. So what do we have in the first frame? A blank frame? But is that frame a part of the video or just something unknown. In videos with the blank frame, we can say it took 1/7 seconds for the actual first frame with the picture to appear, but if the video directly starts with the frame with picture as its first frame, will be treat it differently?

2. The attempt at a solution
I calculated the velocity using the assumption that 7 frames will take 1 second, meaning the time for the first frame is 1/7 seconds. I need the time, as I am calculating the velocity of water, using the flow of beads. I'm using the software ImageJ to analyze the video and the video starts with the first frame being the actual frame with the picture.

My question is, should I treat the time each frame takes as the divisions of a measuring stick/ruler, having a starting point and an ending point, and 1/7 second being the time taken for the frame to go from the starting point to the ending point? However, if we look at each frame, they are just stationary pictures and as far as I know, stationary pictures don't have the dimension of time. I am really confused about this. Please can someone help??

2. Feb 7, 2015

### Nathanael

Seven frames will still correspond to 1 second, but it will be the eighth frame that corresponds to 1 second since frame 1. So 2 seconds (since frame 1) would be the 15th frame, 3 seconds (since frame 1) would be frame 22, and so on.

3. Feb 7, 2015

### Fizz1cks

Thank you for replying. I see what you mean. Lets see it in a calculation. I found the distance traveled by a tiny bead in water to be 110.2 microns at the seventh frame (7 frames per second). So, if the eighth frame corresponds to 1 second, then the total time the bead traveled in 7 frames will be 0.857 seconds instead of 1 second. So, it's velocity will be 128.6 microns per second?

Distance travel in 7 frames: 110.2 microns
Total time taken in 7 frames: 0.857 seconds

Velocity= 110.2 microns / 0.857 seconds => 128.6 microns per second?

or,
Distance travel in 7 frames: 110.2 microns
Total time taken in 7 frames: 1 seconds

Velocity= 110.2 microns / 1 seconds =>110.2microns per second?

Last edited: Feb 7, 2015
4. Feb 7, 2015

### Nathanael

Yes this is correct. As long as the video was not slowed down or sped up (it should be played at the same frames per second as it was recorded).

In general, the time between frames n and m is $T=\frac{m-n}{7}$ seconds. (Assuming 7 FPS)
In the situation you just described, n=1 and m=7, so T=6/7 seconds.

5. Feb 7, 2015

### Fizz1cks

Ahh I see now, it makes total sense. Thank you for your help!