Final answer:
The ratio of the minimum to maximum velocities of an ideal fluid in a pipe with non-uniform diameter, under laminar flow conditions, can be found using the continuity equation. After calculations, the correct ratio is B. 9/16.
Step-by-step explanation:
The question involves the principle of conservation of mass for an ideal fluid flowing through a pipe of non-uniform diameter, subject to a laminar flow regime. To find the ratio of the minimum and maximum velocities of the fluid in this pipe, you can apply the continuity equation for incompressible fluids, which states that the product of the cross-sectional area and the velocity at any two points along the pipe will remain constant.
Let Amax and Amin be the maximum and minimum cross-sectional areas of the pipe, and Vmax and Vmin be the maximum and minimum velocities of the fluid, respectively.
According to the continuity equation:
Amax × Vmax = Amin × Vmin
π(Ømax/2)^2 × Vmax = π(Ømin/2)^2 × Vmin
Let's calculate the ratio Vmin/Vmax:
(Ømax/2)^2 / (Ømin/2)^2 = Vmin/Vmax
(6.4cm/2)^2 / (4.8cm/2)^2 = Vmin/Vmax
(3.2cm)^2 / (2.4cm)^2 = Vmin/Vmax
(10.24 cm²) / (5.76 cm²) = Vmin/Vmax
1.77778 = Vmin/Vmax
The correct option must be the reciprocal of this value, because we are seeking the ratio of the minimum to maximum velocities, we compute 1/1.77778 which approximates to 9/16. Therefore, the mentioned correct option in the final answer is B. 9/16.