**Core Concept**
The velocity of blood flow in a blood vessel is determined by the pressure gradient and the resistance offered by the vessel's walls. It is an essential concept in hemodynamics, which is the study of the dynamics of blood flow through the circulatory system.

**Why the Correct Answer is Right**
The velocity of blood flow is calculated using the formula: velocity = flow rate / cross-sectional area. In a blood vessel, the flow rate is determined by the pressure gradient and the resistance offered by the vessel's walls. The most significant factor influencing velocity is the radius of the vessel, as it affects the cross-sectional area and the resistance to flow. According to Poiseuille's law, the velocity of blood flow is inversely proportional to the fourth power of the radius of the vessel. This means that even small changes in the radius of a blood vessel can significantly affect the velocity of blood flow.

**Why Each Wrong Option is Incorrect**
**Option A:** Velocity of blood flow is directly proportional to the radius of the vessel. This is incorrect because, according to Poiseuille's law, velocity is inversely proportional to the fourth power of the radius.
**Option B:** The velocity of blood flow is independent of the pressure gradient. This is incorrect because the pressure gradient is a critical factor in determining the flow rate and, subsequently, the velocity of blood flow.
**Option C:** The velocity of blood flow is directly proportional to the cross-sectional area of the vessel. This is incorrect because the velocity is inversely proportional to the cross-sectional area, as per the formula: velocity = flow rate / cross-sectional area.

**Clinical Pearl / High-Yield Fact**
In clinical practice, it's essential to remember that even small changes in blood vessel diameter can significantly affect blood flow and, consequently, tissue perfusion. This is why conditions like atherosclerosis, which cause narrowing of blood vessels, can lead to ischemia and tissue damage.

**Correct Answer: C. The velocity of blood flow is inversely proportional to the fourth power of the radius of the vessel.