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Let’s say this odd design, the arrow is the direction of water flow (don’t ask why because I’m just curious about it)...

I drew this out and just wanted to ask if water were to flow into the pipe like that, will there be entrance losses ?

I know if water were to flow the opposite direction, and the exit pipe goes into the water as a submerged exit, there are exit losses.

But now I reverse the direction of flow and now, so is there entrance losses ?

enter image description here

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Whichever end you use as the intake will have entry losses - a suitable entrance is a “bell end” or rounded.

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Yes, there are entrance losses. Pretty significant entrance losses compared to some other entrance designs, in fact. @PJNoess gives some excellent information on why you should expect entrance losses in the situation you drew. To calculate the losses one method is to use the K method, described here and summarized below.

Headloss in the pipe is calculated as: $$h_p = f\frac{L}{D}\frac{V^2}{2g}$$ where $f$ is the friction factor found on a Moody diagram, $L$ is the length, $D$ is the diameter, $V$ is the velocity, and $g$ is the gravitational constant.

Minor losses are from entrances, exits, valves, bends, nozzles, etc. They can be calculated as $$h_m = K\frac{V^2}{2g}$$ where $K$ is the sum of the coefficients for the minor loss. Some $K$ values for entrances can be looked up here.

You drew an inward projecting entrance, which has: $K=0.78$

A flush entrance like the exit on your drawing would have $K=0.5$ if used as an entrance ($K=1$ for all exits).

A rounded entrance with a large radius can have $K$ as low as $0.04$

Lower $K$ values mean lower losses. An inward projecting entrance has high losses compared to many other designs.

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There are most definitely entrance losses, and the configuration you've shown would have the greatest losses. Basically, drawing streamlines that represent how a fluid would flow into the pipe gives you a good idea of how severe the losses would be. In your example some of the fluid would have to flow down alongside your projecting pipe then do a U-turn to enter the pipe. The horizontal velocity as it enters the pipe would cause a constriction in the flow, resulting in very high losses.

On the other hand, if the flow entering the pipe was from the face of a smooth plate with a large radius leading to a gradual narrowing of the flow field, the streamlines would gradually merge and the losses would be much, much less, on the order of 20x less than the example you have shown.

Likewise, if you reverse the direction of the flow in your diagram, the entrance is now at the bottom and there would be a square edged entrance to the pipe flow. The losses in this case would be intermediate between the two cases above.

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