Final answer:
The pressure difference between the two ends of a horizontal tube through which glycerine flows can be calculated using Poiseuille's Law. After computing the volumetric flow rate from the given mass flow rate and density, the pressure difference is found to be approximately 0.325 N/m², corresponding to option B.
Step-by-step explanation:
The student is asking about the calculation of pressure difference in a horizontal tube through which glycerine flows, applying the principles of fluid dynamics, particularly the Poiseuille's Law, which relates pressure difference, flow rate, viscosity, length, and radius of the tube. To find the pressure difference (ΔP) between the two ends of a tube, we need to use the following form of Poiseuille's Law: ΔP = (8 * μ * L * Q) / (π * r^4)
Where:
- ΔP is the pressure difference
- μ is the dynamic viscosity of the fluid
- L is the length of the tube
- Q is the volumetric flow rate
- r is the radius of the tube
- π is Pi, approximately 3.14159
First, we need to calculate the volumetric flow rate (Q). Since the mass flow rate is given as 4.0 x 10^-5 kg/s and the density (ρ) of glycerine is 13 x 10^3 kg/m³, we can find Q using Q = mass flow rate / density.
Q = (4.0 x 10^-5 kg/s) / (13 x 10^3 kg/m³) = 3.077 x 10^-9 m³/s
Now we can substitute the values into Poiseuille's equation:
ΔP = (8 * 0.83 Ns/m² * 15 m * 3.077 x 10^-9 m³/s) / (3.14159 * (0.10 m)^4)
ΔP ≈ 0.325 N/m²
Therefore, the pressure difference between the two ends of the tube is approximately 0.325 N/m², which corresponds to option B.