Final Answer:
The volume flow rate of the fluid through the tube is 1.35*10^-6 ± 2.25*10^-9 m^3/s.
Step-by-step explanation:
The volume flow rate, Q, of a fluid through a tube can be calculated using the formula:
Q = v * A
where v is the velocity of the fluid and A is the cross-sectional area of the tube. In our case, we know the velocity, v, which is given as 0.75*10^-9 m^3/s, and we can calculate the cross-sectional area, A, using the radius, r:
A = πr^2
Substituting our values for v and r into the formula for Q, we get:
Q = 0.75*10^-9 * π * (0.006 ± 0.00015)^2 m^3/s
Simplifying this expression and rounding to three significant figures, we obtain our final answer: Q = 1.35*10^-6 ± 2.25*10^-9 m^3/s. The uncertainty in Q is calculated using the propagation of uncertainty formula:
δQ = sqrt(δv^2 + v^2 * δA^2)
where δv and δA are the uncertainties in velocity and cross-sectional area, respectively. Using our given uncertainties for v and r, we can calculate δA as follows:
δA = 2 * r * δr = 2 * (0.006 ± 0.00015) * (0.00015) m^2/s
Substituting this into the formula for δQ and simplifying, we get:
δQ = sqrt(δv^2 + v^2 * (4 * r * δr)^2) = sqrt(10^4 * (4 * (6*10^-6) * (1.5*10^-6))^2) m^3/s = 2.25*10^-9 m^3/s.