ANS:A - 9100

The Reynolds number (Re) is defined as the ratio of inertial forces to viscous forces in a fluid flow and is given by the formula: Re=μρ×V×D​ Where:

• ρ is the density of the fluid,
• V is the velocity of the fluid,
• D is the diameter of the pipe, and
• μ is the dynamic viscosity of the fluid.

Given that the Reynolds number (Re) for the initial flow conditions is 10000, and the fluid velocity is decreased by 30% and the pipe diameter is increased by 30%, let's denote the new velocity as ′V′ and the new diameter as ′D′. According to the given changes:

• The new velocity ′V′ will be 0.7×0.7×V (decreased by 30%),
• The new diameter ′D′ will be 1.3×1.3×D (increased by 30%).

Substituting these values into the Reynolds number formula, we get: Re′=μρ×(0.7×V)×(1.3×D)​ Re′=μρ×0.7×1.3×V×D​ Re′=μ0.91×ρ×V×D​ Re′=0.91×Re Thus, the new Reynolds number ′Re′ will be 91% of the original Reynolds number Re. Therefore, the new Reynolds number is 0.91×10000=91000.91×10000=9100. So, the correct answer is 9100.