Details that are not provided: the problem figure is included.
We can address the exercise by applying Poiseuille's law. This law indicates that for a fluid flowing in a laminar manner within a confined pipe,
where:
represents the pressure difference across the two ends
denotes the viscosity of the fluid
L signifies the length of the pipe
indicates the volumetric flow rate, where
is the cross-sectional area of the tube and
refers to the fluid's velocity
r stands for the pipe's radius.
This law can be utilized for the needle, allowing us to compute the pressure difference between point P and the needle's end. In this scenario, we have:
is the dynamic viscosity of water at
L=4.0 cm=0.04 m
and r=1 mm=0.001 m
Substituting these values into the formula yields:
This pressure difference specifies the value between point P and the needle's termination. As the end of the needle is under atmospheric pressure, the gauge pressure at point P, relative to atmospheric pressure, is exactly 3200 Pa.
