Final answer:
The new flow rates after the changes in pressure difference, viscosity, length, and radius of the tube are calculated using Poiseuille's Law, with each factor affecting the flow rate in different ways, resulting in new flow rates of 150 cm³/s, 33.3 cm³/s, 25 cm³/s, 0.01 cm³/s, and 3.75 cm³/s for the given scenarios.
Step-by-step explanation:
The subject of this question falls under the category of Physics, specifically fluid dynamics. The question is typically at the college level, given the complexity of the physics principles involved. The fluid flow through a tube is governed by Poiseuille's Law, which states: Q = (πΔP r^4) / (8ηL), where Q is the volume flow rate, ΔP is the pressure difference, r is the radius of the tube, η is the viscosity of the fluid, and L is the length of the tube.
(a) If the pressure difference increases by a factor of 1.50, the flow rate will also increase by the same factor (assuming a linear relationship), resulting in a new flow rate of 1.50 x 100 cm³/s = 150 cm³/s.
(b) Substituting a fluid with a viscosity 3.00 times greater will decrease the flow rate by a factor of 3.00, giving a new flow rate of 100 cm³/s / 3.00 = 33.3 cm³/s.
(c) Using a tube 4.00 times the length will reduce the flow rate by a factor of 4.00, thus the new flow rate is 100 cm³/s / 4.00 = 25 cm³/s.
(d) A tube with a radius 0.100 times the original implies the radius is reduced to one-tenth, and since flow rate depends on the fourth power of the radius, the new flow rate will be (0.100)^4 x 100 cm³/s = 0.01 cm³/s.
(e) With a radius 0.100 times the original and half the length, and the pressure difference increased by a factor of 1.50, the flow rate will be (0.100)^4 x 100 cm³/s / 0.5 x 1.50 = 3.75 cm³/s.