To solve this problem, we will use Bernoulli's equation, a simplified form of the law of conservation of energy. It applies to fluids that are incompressible (constant density) and non-viscous.

Bernoulli's equation is: 

Where  is pressure,  is density,  is the gravitational constant,  is velocity, and  is the height. Since the height of the pipe is constant, we can eliminate the height term leaving us with:

The velocity is increasing, making the velocity term negative. We are subtracting some amount from , therefore , meaning the pressure is decreasing.

In this question, we're presented with a scenario in which blood is flowing through a blood vessel with a clot. We're asked to determine how the partial pressure of oxygen changes as the blood flows pass the clot. To answer this, we'll need to understand the concepts of the continuity equation, Bernoulli's equation, and partial pressures.

Since the blood is flowing past an obstruction, and because the volume flow rate is the same everywhere, we can use the continuity equation to show the relationship between velocity and area.

What this equation shows is that, when the volume flow rate is constant, the velocity of the fluid is inversely proportional to the area in which it is flowing. When the blood passes through the narrow space caused by the obstruction, it temporarily speeds up and thus has a higher velocity.

Next, we can use the Bernoulli equation to show how the velocity is related to pressure.

In this case, we can assume that the height does not change, and thus we can take the potential energy component out of the equation. What we are left with is an inverse relationship between velocity and pressure. Thus, as the velocity increases, the pressure decreases.

The next thing to do is relate total pressure with partial pressure. Remember that partial pressure refers to the proportion of pressure that a certain gas contributes to the overall pressure when there is a mixture of gasses. For instance, the partial pressure of oxygen in the atmosphere is roughly , meaning that oxygen is responsible for contributing  of the overall pressure of the atmosphere. The expression for partial pressure is as follows.

Again, what this means is that the partial pressure of a certain gas is dependent on both the fraction of that gas out of all other gasses present, and also the total pressure. Even though the proportion of oxygen will remain the same as blood flows pass the clot, the total pressure in that region decreases. Thus, the partial pressure of oxygen in this region will decrease as well.

All in all, let's summarize what happened by bringing it all together. As the blood flows through a narrower space due to the obstruction, its velocity increases. As a result of the increase in velocity, the pressure lessens. And as the pressure decreases, so too does the partial pressure of any of the gasses within that region, including that of oxygen.

The correct answer is molasses. Since this liquid is notably thicker and more difficult to move, it is intuitively sensed that is has the highest viscosity of this group of fluids. 

We will start with Newton's second law:

Since the block is sinking at a constant velocity, we know that the net force is 0:

There are three forces acting on the ball: gravitational, buoyant, and drag. If we designate any downward force as positive, we get:

 (1)

Where:

 (2)

Where:

 (3)

 (4)

Plugging expressions 2, 3, and 4 into 1, we get:

Now we need to rearranging for the drag coefficient:

Plugging in our values, we get:

We will start with Newton's second law for this problem:

When the ball reaches terminal velocity, we know that the net force on the ball is equal to 0:

There are three forces acting on the ball: gravitational, buoyant, and drag. If we designate any downward force as positive, we get:

 (1)

Where:

 (2)

Where:

 (3)

 (4)

Substituting expressions (2), (3), and (4) into (1), we get:

Now we just need to rearranging for velocity.

We have all of these values, so time to plug and chug: