Answer:
97 cP
Explanation:
Use the Hagen-Poiseuille equation, also known as Poiseuille's law:
ΔP = 8μLQ / πR⁴
where ΔP is the pressure drop,
μ is the dynamic viscosity,
L is the length of the pipe,
Q is the volumetric flow rate,
and R is the radius of the pipe.
Convert all units to SI units:
ΔP = ρgh
ΔP = (13.6 g/cm³) (9.8 m/s²) (18 cm) × (1 kg / 1000 g) (100 cm/m)²
ΔP = 23,990 N/m²
L = 8 cm × (1 m / 100 cm)
L = 0.08 m
Q = 13 cm³/min × (1 m / 100 cm)³ (1 min / 60 s)
Q = 2.167×10⁻⁷ m³/s
R = (1.30 mm / 2) × (1 m / 1000 mm)
R = 6.5×10⁻⁴ m
Now plug in and solve for μ.
ΔP = 8μLQ / πR⁴
μ = πR⁴ΔP / 8LQ
μ = π (6.5×10⁻⁴ m)⁴ (23,990 N/m²) / 8 (0.08 m) (2.167×10⁻⁷ m³/s)
μ = 0.097 Pa·s
μ = 97 mPa·s = 97 cP
