Experimentally Measuring the Velocity of Water coming out of an Orifice I plan on doing an investigation into Torricelli's Law, where I will be looking at one of the following:

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*How the cross-sectional area of an orifice affects the velocity of water coming out of it (constant height).


*How the height of an orifice affects the velocity of water coming out of it (constant orifice area).
However, I was unsure about how to accurately measure the velocity of water coming out of the orifice. Videos on YouTube only suggest one method, which is using the horizontal and vertical displacements of the water stream to calculate velocity. However, when I've done this experimentally I've found an about $15\%$ error compared to expected values. The process is also not very exact per se, i.e. it is hard to judge the exact marking of a ruler that the stream lands on.
Therefore, I was wondering if there were any accurate means to measure the velocity of water coming out of an orifice, using equipment typically found in a school laboratory.
 A: A simple method to get a more precise location of where the water stream intersects a plane is by letting it fall through the plane and to intercept the two edges of the stream with a sharp edge. Even small disturbances of the stream by the edge should be easily noticeable. I would guestimate that you will get sub-mm precision from that, i.e. well below 1% errors on the velocity if done well. A physicist I knew once did the opposite: he let the water stream intercept a beam of light (a slotted optocoupler sensor costs less than a dollar these days) and regulated the height in the reservoir using that signal. I think he got better than 0.1% errors out of that setup.
A: With a "high speed" camera, and assuming a near laminar flow, you could cut the flow with something like a fan blade and measure that edge created using a scale behind the water with respect to the camera.
Another is if you used a plunger (imagine a large syringe) then you can measure its position which directly gives you changes in volume.  The plunger friction creates an unknown to your pressure though.
A: Water is incompressible. So you can put a bucket under your stream and let it run for some time. That way you measure the volume of water coming out per time [units m$^3/$s]. Divide by the cross-sectional area of the orifice [m$^2$] to get the water speed [m$/$s].
A: I did some work on this once and came across a range of references on this topic.  I can't remember if they specifically cover what you ask for here, but might be in one of these:
Paulo Murilo Castro de Oliveira, Antonio Delfino, Eden Viera Costa and Carlos Alberto Faria Leite,“Pin-hole water flow from cylindrical bottles”, Phys. Educ. 35 110 (March 2000)
Rod Cross, “Filling or draining a water bottle with two holes”, Phys. Educ. 51 045014 (July 2016).
Stephen M. Durbin, “Combined demonstration of non-viscous and viscous flow”, Am. J. Phys. 87(47), 305 (March 2019).
Laura Pavesi, “Investigating Torricell’s Law (and More) with a 19th-Century Bottle”, Phys. Teach.57, 106 (January 2019).
A: Place a measurement grid by the stream and start filming. As clear water flows, add food color to the water. Measure the movement of the front of the colored water versus the grid. Preferably, use clear pipes to allow measurement of the water velocity before it leaves the orifice.
