Physics, 26.12.2019 05:31 Brook211

100-ft-long horizontal pipeline transporting benzene develops a leak 43 ft from the high-pressure end. the diameter of the leak is estimated to be 0.1 in. at the time, the upstream pressure in the pipeline is 50 psig and the downstream pressure is 40 psig. estimate the mass flow rate of benzene through the leak. the specific gravity of benzene is 0.8794.

Answers: 1

Show answers

Answers

Answer from: laurieburgess804

Explanation:

The mass flow rate of benzene from the leak in the pipeline containing benzene is:

$Q_m=AC_o\sqrt{2\rho g_cP_g}$

Here, Q_m is the mass flow rate through the leak of the pipeline. is the area of the hole, C_o is the discharge rate, $\rho$ is the fluid density, g_c is the gravitational constant and P_g is the constant gauge pressure within the process unit.

The diametre of the leak (d) is 0.1 in. Convert from in to ft.

$d=(0.1 in)(\frac{1ft}{12in})\\=8.33\times 10^{-3}ft$

Calculate the area (A) of the hole. The area of the hole is.

$A=\frac{\pi d^2}{4}$

Substitute 3.14 for $\pi$ and $8.33\times 10^{-3}ft$ for d and calculate A.

$A=\frac{\pi d^2}{4}\\\\\frac{(3.14)(8.33\times 10^{-3})^2}{4}\\\\5.45\times 10^{-5}ft^2$

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 $62.4\frac{Ib_m}{ft^3}$ . Calculate density of benzene.

Density of benzene = specific gravity of benzene x density of reference substance

$=(0.8794)(62.4\frac{Ib_m}{ft^3})\\\\54.9\frac{Ib_m}{ft^3}$

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

P_g =+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 P_g .

Upstream x distance from upstream pressure end

P_g =+DOWNSTREAM PRESSURE X DISTANCE FROM THE DOWNSTREAM PRESSURE END/ TOTAL LENGTH OF THE HORIZONTAL PIPELINE

$=\frac{(50psig\times 43ft)+(40psig \times 57ft)}{100ft}\\\\=44.3psig$

Convert the pressure from psig to Ib_f/ft^2

$P_g=(44.3psig)(\frac{1\frac{Ib_f}{ft^2}}{1psig})(144\frac{in^2}{ft^2})\\\\=6,379.2\frac{Ib_f}{ft^2}$

The leak is like a sharp orifice. Take the value of the discharge coefficient as 0.61.

Substitute $5.45\times 10^{-5}ft^2$ for A. 0.61 for C_o , $54.9\frac{Ib_m}{ft^3}$ for $\rho$ , $32.17\frac{ft.Ib_m}{Ib_f.s^2}$ for g_c , and $6,379.2\frac{Ib_f}{ft^2}$ for P_g and calculate Q_m

$Q_m=AC_o\sqrt{2\rho g_cP_g}\\\\=(5.45\times 10^{-5}ft^2)(0.61)\sqrt{2(54.9\frac{Ib_m}{ft^3})(32.17\frac{ft.Ib_m}{Ib_f.s^2})(6,379.2\frac{Ib_f}{ft^2})}\\\\(3.3245\times 10^{-5}ft^2)\sqrt{22,533,031.21\frac{Ib^2_m}{ft^4.s^2}}\\\\=0.158\frac{Ib_m}{s}$

The mass flow rate of benzene through the leak in the pipeline is $0.158\frac{Ib_m}{s}$

Answer from: Quest

the part of the wave he is travelling on is the crest

Answer from: Quest

im srry but ur wrong the answer is d a smooth rock, some red dirt, and an empty bird's nest.

Another question on Physics

Physics, 22.06.2019 17:30

Which planet do you think would be easiest for humans to colonize some day?

Answers: 1

Answer

Physics, 22.06.2019 18:30

Adolphin emits ultrasound at 100khz and uses the timing of reflections to determine the position of objects in the water. part a what is the wavelength of this ultrasound? assume that temperature of water is 20 degrees c. answer in cm

Answers: 2

Answer

Physics, 22.06.2019 19:30

The ability to make things happen is also called a. heat b. force c. matter d. energy

Answers: 1

Answer

Physics, 23.06.2019 02:00

Two technicians are discussing a starter that clicks repeatedly when the key is turned to the crank position. technician a says the solenoid hold-in winding is open. technician b says the solenoid pull-in winding is open. who is correct?

Answers: 2

Answer

You know the right answer?

100-ft-long horizontal pipeline transporting benzene develops a leak 43 ft from the high-pressure en...

Questions