This is an arch, its basically a half circle attach to a rectangle, you could also think of it as an upside down U. A dome is a Sphere with the inside hollowed out.
1 difference is a dome is a 3 dimensional shape while an arch is normally not. Or that a dome is the complete shape with a arch act as it’s diameter.
Answer:
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Answer:
Flow rate is ![1.82\times 10^{-8} m^{3}/s](https://tex.z-dn.net/?f=1.82%5Ctimes%2010%5E%7B-8%7D%20m%5E%7B3%7D%2Fs)
Explanation:
Given information
Density of oil, ![\rho_{oil}= 850 Kg/m^{3}](https://tex.z-dn.net/?f=%5Crho_%7Boil%7D%3D%20850%20Kg%2Fm%5E%7B3%7D)
kinematic viscosity, ![v= 0.00062 m^{2} /s](https://tex.z-dn.net/?f=v%3D%200.00062%20m%5E%7B2%7D%20%2Fs)
Diameter of pipe, D= 5 mm= 0.005 m
Length of pipe, L=40 m
Height of liquid, h= 3 m
Volume flow rate for horizontal pipe will be given by
where
is dynamic viscosity and
is pressure drop
At the bottom of the tank, pressure is given by
![P_{bottom}=\rho_{oil} gh=850 Kg/m^{3}\times 9.81 m/s^{2}\times 3 m= 25015.5 N/m^{2}](https://tex.z-dn.net/?f=P_%7Bbottom%7D%3D%5Crho_%7Boil%7D%20gh%3D850%20Kg%2Fm%5E%7B3%7D%5Ctimes%209.81%20m%2Fs%5E%7B2%7D%5Ctimes%203%20m%3D%2025015.5%20N%2Fm%5E%7B2%7D)
Since at the top pressure is zero, therefore change in pressure a difference between the pressure at the bottom and the top. It implies that change in pressure is still ![25015.5 N/m^{2}](https://tex.z-dn.net/?f=25015.5%20N%2Fm%5E%7B2%7D)
Dynamic viscosity, ![\mu=\rho_{oil}v= 850 Kg/m^{3}\times 0.00062 m^{2}/s=0.527 Kg/m.s](https://tex.z-dn.net/?f=%5Cmu%3D%5Crho_%7Boil%7Dv%3D%20850%20Kg%2Fm%5E%7B3%7D%5Ctimes%200.00062%20m%5E%7B2%7D%2Fs%3D0.527%20Kg%2Fm.s)
Now the volume flow rate will be
![\bar v=\frac {25015.5 N/m^{2}\times \pi \times 0.005^{4}}{128\times 0.527 Kg/m.s \times 40}=1.82037\times 10^{-8} m^{3}/s\approx 1.82\times 10^{-8} m^{3}/s](https://tex.z-dn.net/?f=%5Cbar%20v%3D%5Cfrac%20%7B25015.5%20N%2Fm%5E%7B2%7D%5Ctimes%20%5Cpi%20%5Ctimes%200.005%5E%7B4%7D%7D%7B128%5Ctimes%200.527%20Kg%2Fm.s%20%5Ctimes%2040%7D%3D1.82037%5Ctimes%2010%5E%7B-8%7D%20m%5E%7B3%7D%2Fs%5Capprox%201.82%5Ctimes%2010%5E%7B-8%7D%20m%5E%7B3%7D%2Fs)
Proof of flow being laminar
The velocity of flow is given by
![V_{flow}=\frac {\bar v}{A}=\frac {1.82\times 10^{-8} m^{3}/s}{0.25\times \pi\times 0.005^{2}}=0.000927104 m/s](https://tex.z-dn.net/?f=V_%7Bflow%7D%3D%5Cfrac%20%7B%5Cbar%20v%7D%7BA%7D%3D%5Cfrac%20%7B1.82%5Ctimes%2010%5E%7B-8%7D%20m%5E%7B3%7D%2Fs%7D%7B0.25%5Ctimes%20%5Cpi%5Ctimes%200.005%5E%7B2%7D%7D%3D0.000927104%20%20m%2Fs)
Reynolds number, ![Re=\frac {\rho_{oil} v_{flow} D}{\mu}=\frac {850 Kg/m^{3}\times 0.000927104 m/s\times 0.005}{0.527 kg/m.s}=0.007476648](https://tex.z-dn.net/?f=Re%3D%5Cfrac%20%7B%5Crho_%7Boil%7D%20v_%7Bflow%7D%20D%7D%7B%5Cmu%7D%3D%5Cfrac%20%7B850%20Kg%2Fm%5E%7B3%7D%5Ctimes%200.000927104%20m%2Fs%5Ctimes%200.005%7D%7B0.527%20kg%2Fm.s%7D%3D0.007476648)
Since the Reynolds number is less than 2300, the flow is laminar and the assumption is correct.
Answer:
i) 796.18 N/mm^2
ii) 1111.11 N/mm^2
Explanation:
Initial diameter ( D ) = 12 mm
Gage Length = 50 mm
maximum load ( P ) = 90 KN
Fractures at = 70 KN
minimum diameter at fracture = 10mm
<u>Calculate the engineering stress at Maximum load and the True fracture stress</u>
<em>i) Engineering stress at maximum load = P/ A </em>
= P /
= 90 * 10^3 / ( 3.14 * 12^2 ) / 4
= 90,000 / 113.04 = 796.18 N/mm^2
<em>ii) True Fracture stress = P/A </em>
= 90 * 10^3 / ( 3.24 * 10^2) / 4
= 90000 / 81 = 1111.11 N/mm^2
Answer:
Explanation:
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