what is the direction of blood flow in relation to the direction of water flow over the gills

To be efficient, a fish applies the counter-current principle, i.e. the most oxygen-poor blood will extract the remaining oxygen from the most "stale" part of the water stream.

Does that tell you which is the direction of blood flow?

The direction of blood flow in relation to the direction of water flow over the gills is countercurrent. This means that the flow of blood is in the opposite direction to the flow of water.

Now, let me explain how this countercurrent system works. In aquatic animals such as fish, oxygen is obtained from the water by passing it over specialized structures called gills. The gills contain small blood vessels called capillaries. When water flows over the gills, there is a concentration gradient of oxygen between the water and the blood.

In a countercurrent system, blood flows through the gill capillaries in the opposite direction to the flow of water. This arrangement maximizes the exchange of oxygen between the water and the blood.

As water enters the fish's mouth, it flows over the gill filaments. Blood that contains carbon dioxide and has depleted oxygen levels enters the gill capillaries. At the same time, oxygen-rich water flows over the gills.

Because the blood flows in the opposite direction to the water, oxygen continuously diffuses from the water to the blood as long as there is a concentration gradient. This allows for efficient oxygen uptake by the blood. By the time the blood reaches the end of the gill filaments, it has acquired a significant amount of oxygen and has released carbon dioxide into the water.

The countercurrent flow of blood and water helps to maintain the concentration gradient for oxygen uptake throughout the entire length of the gill system, ensuring efficient gas exchange for the fish.