Practice Problems $-$ Fall $2024$

The pressure at the top of a tank of jet fuel is $180\mathrm{.}6{10}^3\frac{N}{m^2}.$ The depth of liquid in the tank is

$6\mathrm{.}4$ m $.$ The density of the fuel is $825k\frac{g}{m^3}.$

Calculate the head of liquid meters which corresponds to the absolute pressure at the bottom of

the tank.

Two parallel plates that are $0\mathrm{.}00914$ m apart have the distance between them filled with

soybean oil. The lower plate is pulled at a relative velocity $0\mathrm{.}366\frac{m}{s}$ greater than the top plate.

The viscosity of the soybean oil is $4{10}^{-2}$ Pa$.$s$.$

i$.$ Calculate the shear stress and the shear rate using lb force, ft and s units $($English

engineering units$).$ Answers: $3\mathrm{.}34{10}^{-2}l\frac{b_f}{f}{t}^2$ and $40\mathrm{.}0s^{-1}$

ii$.$ If glycerol with a viscosity of $1\mathrm{.}069k\frac{g}{m}.s$ is used instead of soybean oil, $($i$)$ what relative

velocity in $\frac{m}{s}$ is needed using the same distance between the plates for the same shear

stress, and $($ii$)$ what is the new shear rate?

In a natural$-$gas pipeline at station $1,$ the pipe diameter is $2$ ft $,$ and the flow conditions are $800$

$a,70F$ and $50f\frac{t}{s}$ velocity. At station $2,$ the pipe diameter is $3$ ft $,$ and the flow conditions are

$500$ psia and $70F.$ Assume natural gas is methane. $($a$)$ What is the velocity at station $2?($b$)$

What is the mass flow rate?

$($I would like to know the steps to solve each questions$)$