Final answer:
Using the Hagen-Poiseuille law, a 5.00% decrease in tube radius results in a flow decrease of approximately 18.55%, which is very close to the stated 19.0%. Similarly, a 5.00% increase in radius would yield an approximated flow increase of 21.55%.
Step-by-step explanation:
To verify whether a 19.0% decrease in laminar flow through a tube is caused by a 5.00% decrease in radius, we can use the Hagen-Poiseuille law which describes laminar flow in a cylindrical tube: Q = (πΔP r^4) / (8ηl), where Q is the flow rate, ΔP is the pressure difference, r is the radius, η is the viscosity, and l is the length of the tube. According to this equation, flow rate (Q) is proportional to the fourth power of the radius.
When the radius (r) decreases by 5.00%, the new radius becomes 0.95r. Plugging this into the law, we get the new flow rate Q' = (πΔP (0.95r)^4) / (8ηl) = Q (0.95)^4 ≈ Q (0.8145) which is a decrease of approximately 18.55%. This is very close to the given 19.0% decrease, thereby supporting the statement (assuming the calculation was not assuming an already rounded 5% decrease).
Conversely, for a 5.00% increase in radius, we get the new flow rate Q" = (πΔP (1.05r)^4) / (8ηl) = Q (1.05)^4 ≈ Q (1.2155), meaning the flow would increase by approximately 21.55%.