Harmonics problem. A square wave of frequency f contains harmonics (sine waves) at f, 3f, 5f, 7f, ... . Suppose a system respond
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Answer:
Explanation:
The mass flow rate of benzene from the leak in the pipeline containing benzene is:
Here, is the mass flow rate through the leak of the pipeline.
is the area of the hole,
is the discharge rate,
is the fluid density,
is the gravitational constant and
is the constant gauge pressure within the process unit.
The diametre of the leak (d) is 0.1 in. Convert from in to ft.
Calculate the area (A) of the hole. The area of the hole is.
Substitute 3.14 for and
for d and calculate A.
The specific gravity of benzene is 0.8794. Specific gravity is the ratio of th density of a substance to the density of a reference substance.
Specific gravity of benzene = density of benzenee/denity of reference substance
Rewrite the expression in terms of density of benzene.
Density of benzene = specific gravity of benzene x density of reference substance
Take the reference substance as water. Density of water is . Calculate density of benzene.
Density of benzene = specific gravity of benzene x density of reference substance
Calculate the pressure at the point of leak. The pressure is the average of the pressure of the high and low pressure end. Write the expression to calculate the average pressure.
Upstream x distance from upstream pressure end
=+DOWNSTREAM PRESSURE X DISTANCE FROM THE DOWNSTREAM PRESSURE END/ TOTAL LENGTH OF THE HORIZONTAL PIPELINE
Calculate the distance from the downstream pressure end. The distance from upstream pressure end is 43 ft. Total of the pipe is 100 ft.
Distance from the downstream pressure end = Total length of the pipe - Distance from the upstream pressure end
The distance from upstream pressure end is 43 ft. Total length of the pipe is 100 ft. Substitute the values in the equation.
Distance from the downstream pressure end = Total length of the pipe - Distance from the upstream pressure end
= 100ft - 43ft = 57 ft
Substitute 50 psig for upstream, 43 ft fr distance from the upstream pressure end, 40 psig for downstream pressure, 57 ft for distance from the downstream pressure end, and 100 ft for the total length of the horizontal pipeline and calculate .
Upstream x distance from upstream pressure end
=+DOWNSTREAM PRESSURE X DISTANCE FROM THE DOWNSTREAM PRESSURE END/ TOTAL LENGTH OF THE HORIZONTAL PIPELINE
Convert the pressure from psig to
The leak is like a sharp orifice. Take the value of the discharge coefficient as 0.61.
Substitute for A. 0.61 for
,
for
,
for
, and
for
and calculate
The mass flow rate of benzene through the leak in the pipeline is