Answer:
The pressure difference is [tex]2.01X10^{4} Pa[/tex].
Explanation:
To calculate the pressure difference, we use the fluid-kinetic equation:
Δp = (8μLQ)/(πR⁴)
Step 1: Convert the units of the given terms to SI units:
Diameter = 0.56 cm X ([tex]\frac{1 m}{100 cm}[/tex] = [tex]5.6X10^{-3} m[/tex]
∴ Radius, R = [tex]5.6X10^{-3} /2=2.8X10^{-3} m[/tex]
Length, L = 22 cm X ([tex]\frac{1 m}{100 cm}[/tex] = 0.22 m
Volumetric flow rate, Q = [tex]440X10^{-3} L[/tex] ÷ 2.0 minutes = [tex]220X10^{-3} \frac{L}{min}[/tex]
[tex]220X10^{-3} \frac{L}{min}[/tex] X [tex]\frac{1m^{3} }{1000L}[/tex] X [tex]\frac{1 min}{60 s}[/tex] = [tex]3.67X10^{-6} \frac{m^{3} }{s}[/tex]
Step 2: Input the terms into the fluid-kinetic equation:
Δp = (8 X 0.60 X 0.22 X 3.67[tex]X10^{-6}[/tex]) / (3.142 X ([tex](2.8X10^{-3} )^{4}[/tex])
Δp = 20067.43 Pa = [tex]2.01X10^{4} Pa[/tex].
N.B: The pressure difference is lower than the atmospheric pressure (101300 Pa), which means you can drink the milkshake through the straw.
