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Historical accounts of battles sometimes talk of rivers running red with the blood of fallen combatants.

Many Lancastrians were killed while fleeing; some trampled each other and others drowned in the rivers, which are said to have made them run red with blood for several days. (Wikipedia)

The ensuing massacre of the Parliamentarians is said to have been of such magnitude that the beck ran crimson with blood. (Wikipedia)

This seems implausible, given that a river’s water is flowing, therefore clearing the water of blood eventually. But, it would make a good scene in my story. What is the minimum plausible number of dead bodies it takes to cause a river to be stained in red for days?

Notes:

  • Technology is early medieval, so arrows, stab wounds, and drowning are primary causes of death.
  • The river is medium-size: large enough to drown people but small enough to have people try to flee over it, similar to the Namsen River, in Norway at GPS (64.4464433N,11.8602026E). It is only 130 m across, meriting (failed) attempts by the wounded to swim to safety.
  • The definition of "stained red" is that the water is a solid reddish hue when looked at from above.
  • The stain must last for at least twenty-four hours, over at least a 1km stretch of the river.
  • The river's water color is blue or blue-greenish most of the time.

Other cool numbers:

  • 5 L of blood per person (estimate, usually between 4.7 and 5.7 L)
  • The river speed is about 4-5 mph
  • Blood density is 1060 kg/m³, so it will sink to the bottom eventually.
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    $\begingroup$ I recognize this is similar, but I don't think it's a duplicate. $\endgroup$ – JavaScriptCoder Aug 15 '18 at 0:29
  • $\begingroup$ An important question that hasnt been answered in the answers below: how long does blood stay on the surface? The thickness of viscosity compared to water could mean it flows slower and needs time before it sinks through the faster water below it, meaning you only need to stain a portion of the surface area rather than the entire volume of the river. $\endgroup$ – Demigan Aug 15 '18 at 15:44
  • $\begingroup$ As far as blood density goes, it's not going to be uniform. Exactly what makes it red, and how dense is that? $\endgroup$ – David Thornley Aug 15 '18 at 22:56
  • $\begingroup$ I've accepted an answer that helps me approximate the scale: however having more variables for harder numbers would be nice! $\endgroup$ – JavaScriptCoder Aug 16 '18 at 17:47
  • $\begingroup$ Every time you dilute the blood by 10:1 it becomes twice as potent, at least if you thwack it right. So the real question is how little blood you need to make the river run red. I think one guy rinsing a hangnail would do it, but that may still be too much. But really. the water molecules remember the blood from the War or the Roses, so the river is already red from back then, and the only reason you think it isn’t is the allopathic conspiracy. $\endgroup$ – abarnert Sep 7 '18 at 3:05
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So I was going to add this as a comment, but I don't have the required reputation for that yet; I will try to increase the number of considered factors and variables later.

Based on @candied_orange's anwer and the average discharge rate of $285\:m^3/s$ provided in the link for the river (the German Wikipedia states varying rates between $155\:m^3/s$ and $1000\:m^3/s$), a blood flow of $71,250\:l/s$ is required.

Assuming all of the bodies bleed out entirely, this would require the blood of $14,250$ people to taint the water that flows through the river in a second.

With a speed of $5\:mph$ this would suffice for a stripe of blood-red water that is $2.235\:m$ wide. In order for the taint to be $1\:km$ long, $447.39$ times as much blood would be needed, which would be from roughly $6,375,269$ corpses. Maintining this over a $24\:h$ period would respectively increase this number.

Keep in mind this is a preliminary calculation that assumes the entire water of the river flowing during that time will be tainted with blood to a sufficient degree. What you actually want is probably just the upper layer and enough blood to maintain this before the blood sinks too low to be visible. In general however I recommend using a much, much smaller river, and I don't believe the historic accounts you mentioned refer to a river anywhere near that size either.

Another tip is to utilise dead horses to increase the amount of blood available (1 horse has as much blood as about 8 humans).

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    $\begingroup$ Welcome to the site, psychomap. I can see you will soon be be one of our foremost Blood Mathematicians. $\endgroup$ – kingledion Aug 15 '18 at 15:26
  • $\begingroup$ good job with the calculations and welcome to Worldbuilding.SE! $\endgroup$ – JavaScriptCoder Aug 15 '18 at 15:32
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It all depends on how red is red enough for you.

enter image description here

blood 4-times diluted with water was light red (3)

So if light red is the limit of red enough then you need people bleeding at least one fourth as much blood as the water the river is passing, all over however long you want this to last.

You can find studies about the darnest things.

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    $\begingroup$ Wow, good job finding these things. Looked it up on google — my IP will be on government watch lists for years — and didn’t find it, despite searching “300,000 gallons of blood” and “how much blood is in a human body” and “how much water is needed to dilute blood to colorless” $\endgroup$ – JavaScriptCoder Aug 15 '18 at 2:45

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