If the radius of dentinal tubule is halved, the flow rate will decrease by:
**Core Concept**
The flow rate through dentinal tubules is governed by the Hagen-Poiseuille equation, which states that the flow rate is directly proportional to the fourth power of the radius of the tube. This principle is essential in understanding the fluid dynamics within the dentinal tubules.
**Why the Correct Answer is Right**
When the radius of the dentinal tubule is halved, the cross-sectional area decreases, but the length of the tubule remains the same. According to the Hagen-Poiseuille equation, the flow rate (Q) is inversely proportional to the length of the tube (L) and directly proportional to the fourth power of the radius (r). Since the length remains constant, the decrease in radius from r to r/2 results in a significant decrease in flow rate, proportional to (r/2)^4 = (1/16)r^4. Therefore, the flow rate will decrease by a factor of 16.
**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because the Hagen-Poiseuille equation clearly states that the flow rate is directly proportional to the fourth power of the radius, not the square.
**Option B:** This option is incorrect because the flow rate is inversely proportional to the length of the tube, not directly proportional.
**Option D:** This option is incorrect because it does not accurately reflect the impact of halving the radius on the flow rate.
**Clinical Pearl / High-Yield Fact**
When considering the fluid dynamics within dentinal tubules, remember the Hagen-Poiseuille equation: Q ∝ r^4 / L. This principle is crucial in understanding the effects of various factors on dentinal fluid flow.
**Correct Answer:** C. The flow rate will decrease by a factor of 16.