Rate of flow in tube is V when pressure is P. If the pressure is made four times and radius is halved then what about V

Explanation

According to Poiseuille's Law, the flow rate (V) in a cylindrical tube is directly proportional to the fourth power of the radius of the tube and the pressure difference across the tube, and inversely proportional to the viscosity and length of the tube. Mathematically, this is expressed as:V = (π * r^4 * ΔP) / (8 * η * L)If the pressure is made four times (ΔP becomes 4ΔP) and the radius is halved (r becomes r/2), the new flow rate becomes:New V = (π * (r/2)^4 * 4ΔP) / (8 * η * L) = (π * r^4 * ΔP) / (128 * η * L) = V/4The reduction in radius has a more substantial impact on the flow rate than the increase in pressure, due to the r^4 term, resulting in the flow rate being V/4. Therefore, Option D is correct. Options A, B, and C do not accurately reflect these calculations.