Answer:
14160 kg/m^3
Explanation:
First of all, we need to find the volume of the cylinder.
The volume of the cylinder is given by:
where:
is the radius
is the height
Substituting, we find
And the density is given by
where m = 1 kg is the mass. Substituting, we find
Explanation:
Given that,
Initial volume of tank, V = 6 L
Initial pressure, P = 2 atm
We need to find the final pressure when the air is placed in tanks that have the following volumes if there is no change in temperature and amount of gas:
(a) V' = 1 L
It is a case of Boyle's law. It says that volume is inversely proportional to the pressure at constant temperature. So,
(b) V' = 2500 mL
New pressure becomes :
(c) V' = 750 mL
New pressure becomes :
(d) V' = 8 L
New pressure becomes :
Hence, this is the required solution.
Missing details: figure of the problem is attached.
We can solve the exercise by using Poiseuille's law. It says that, for a fluid in laminar flow inside a closed pipe,
where:
is the pressure difference between the two ends
is viscosity of the fluid
L is the length of the pipe
is the volumetric flow rate, with
being the section of the tube and
the velocity of the fluid
r is the radius of the pipe.
We can apply this law to the needle, and then calculating the pressure difference between point P and the end of the needle. For our problem, we have:
is the dynamic water viscosity at
L=4.0 cm=0.04 m
and r=1 mm=0.001 m
Using these data in the formula, we get:
However, this is the pressure difference between point P and the end of the needle. But the end of the needle is at atmosphere pressure, and therefore the gauge pressure (which has zero-reference against atmosphere pressure) at point P is exactly 3200 Pa.
