Answer:
![z_{2} = 91.640\,m](https://tex.z-dn.net/?f=z_%7B2%7D%20%3D%2091.640%5C%2Cm)
Explanation:
The phenomenon can be modelled after the Bernoulli's Principle, in which the sum of heads related to pressure and kinetic energy on ground level is equal to the head related to gravity.
![\frac{P_{1}}{\rho\cdot g} + \frac{v_{1}^{2}}{2\cdot g}= z_{2}+\frac{P_{2}}{\rho\cdot g}](https://tex.z-dn.net/?f=%5Cfrac%7BP_%7B1%7D%7D%7B%5Crho%5Ccdot%20g%7D%20%2B%20%5Cfrac%7Bv_%7B1%7D%5E%7B2%7D%7D%7B2%5Ccdot%20g%7D%3D%20z_%7B2%7D%2B%5Cfrac%7BP_%7B2%7D%7D%7B%5Crho%5Ccdot%20g%7D)
The velocity of water delivered by the fire hose is:
![v_{1} = \frac{(300\,\frac{gal}{min} )\cdot(\frac{3.785\times 10^{-3}\,m^{3}}{1\,gal} )\cdot(\frac{1\,min}{60\,s} )}{\frac{\pi}{4}\cdot (0.3\,m)^{2}}](https://tex.z-dn.net/?f=v_%7B1%7D%20%3D%20%5Cfrac%7B%28300%5C%2C%5Cfrac%7Bgal%7D%7Bmin%7D%20%29%5Ccdot%28%5Cfrac%7B3.785%5Ctimes%2010%5E%7B-3%7D%5C%2Cm%5E%7B3%7D%7D%7B1%5C%2Cgal%7D%20%29%5Ccdot%28%5Cfrac%7B1%5C%2Cmin%7D%7B60%5C%2Cs%7D%20%29%7D%7B%5Cfrac%7B%5Cpi%7D%7B4%7D%5Ccdot%20%280.3%5C%2Cm%29%5E%7B2%7D%7D)
![v_{1} = 0.267\,\frac{m}{s}](https://tex.z-dn.net/?f=v_%7B1%7D%20%3D%200.267%5C%2C%5Cfrac%7Bm%7D%7Bs%7D)
The maximum height is cleared in the Bernoulli's equation:
![z_{2}= \frac{P_{1}-P_{2}}{\rho\cdot g} + \frac{v_{1}^{2}}{2\cdot g}](https://tex.z-dn.net/?f=z_%7B2%7D%3D%20%5Cfrac%7BP_%7B1%7D-P_%7B2%7D%7D%7B%5Crho%5Ccdot%20g%7D%20%2B%20%5Cfrac%7Bv_%7B1%7D%5E%7B2%7D%7D%7B2%5Ccdot%20g%7D)
![z_{2}= \frac{1\times 10^{6}\,Pa-101.325\times 10^{3}\,Pa}{(1000\,\frac{kg}{m^{3}} )\cdot(9.807\,\frac{m}{s^{2}} )} + \frac{(0.267\,\frac{m}{s} )^{2}}{2\cdot (9.807\,\frac{m}{s^{2}} )}](https://tex.z-dn.net/?f=z_%7B2%7D%3D%20%5Cfrac%7B1%5Ctimes%2010%5E%7B6%7D%5C%2CPa-101.325%5Ctimes%2010%5E%7B3%7D%5C%2CPa%7D%7B%281000%5C%2C%5Cfrac%7Bkg%7D%7Bm%5E%7B3%7D%7D%20%29%5Ccdot%289.807%5C%2C%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D%20%29%7D%20%2B%20%5Cfrac%7B%280.267%5C%2C%5Cfrac%7Bm%7D%7Bs%7D%20%29%5E%7B2%7D%7D%7B2%5Ccdot%20%289.807%5C%2C%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D%20%29%7D)
![z_{2} = 91.640\,m](https://tex.z-dn.net/?f=z_%7B2%7D%20%3D%2091.640%5C%2Cm)
Answer:
The time required to elute the two species is 53.3727 min
Explanation:
Given data:
tA = retention time of A=16.63 min
tB=retention time of B=17.63 min
WA=peak of A=1.11 min
WB=peak of B=1.21 min
The mathematical expression for the resolution is:
![Re_{s} =\frac{2(t_{B}-t_{A})}{W_{A}+W_{B} } =\frac{2*(17.63-16.63)}{1.11+1.21} =0.8621](https://tex.z-dn.net/?f=Re_%7Bs%7D%20%3D%5Cfrac%7B2%28t_%7BB%7D-t_%7BA%7D%29%7D%7BW_%7BA%7D%2BW_%7BB%7D%20%7D%20%3D%5Cfrac%7B2%2A%2817.63-16.63%29%7D%7B1.11%2B1.21%7D%20%3D0.8621)
The mathematical expression for the time to elute the two species is:
![\frac{t_{2}}{t_{1}} =(\frac{Re_{B} }{Re_{s} } )^{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bt_%7B2%7D%7D%7Bt_%7B1%7D%7D%20%3D%28%5Cfrac%7BRe_%7BB%7D%20%7D%7BRe_%7Bs%7D%20%7D%20%29%5E%7B2%7D)
Here
ReB = 1.5
![t_{2} =t_{1} *(\frac{Re_{B} }{Re_{s} } )^{2} =17.63*(\frac{1.5}{0.8621} )^{2} =53.3727min](https://tex.z-dn.net/?f=t_%7B2%7D%20%3Dt_%7B1%7D%20%2A%28%5Cfrac%7BRe_%7BB%7D%20%7D%7BRe_%7Bs%7D%20%7D%20%29%5E%7B2%7D%20%3D17.63%2A%28%5Cfrac%7B1.5%7D%7B0.8621%7D%20%29%5E%7B2%7D%20%3D53.3727min)
Answer:
3 industries that often need the skills of mechanical engineers are:
The key skills mechanical engineers bring to these industries are effective technical skills, the ability to work under pressure, problem-solving skills, creativity and teamwork.
Explanation:
Automotive industry: The skills mechanical engineers bring to automotive industry include designing new cars for development, conducting laboratory testing for performance safety, and troubleshooting design or manufacturing issues with recalled vehicles. Automotive engineers have:
- good mathematical skills, for instance in calculating the stresses power trains and other parts have to withstand;
- understanding and application of principles of physics and chemistry to properly design engines, electrical systems and other car components;
- good computer skills, because 21st century engineers rely on computer-assisted design software;
- knowledge of ergonomics, which is applied in the process of designing a car so that the driver and passengers have a comfortable and functional environment, is another skill mechanical; engineers need.
Construction industry: Mechanical engineers are responsible for designing, building, establishing, and maintaining all kinds of mechanical machinery, tools, and components in the construction industry.
Aerospace industry: Mechanical engineers in aerospace industry produce specifications for design, development, manufacture and installing of new or modified mechanical components or systems. They design more fuel-efficient aircraft that cut emissions and build the fleets of satellites that power modern GPS technology.
Answer:
The answer is as given in the explanation.
Explanation:
The 1st thing to notice is the assumptions required. Thus as the diameter of the cylinder and the wind tunnel are given such that the difference is of the orders of the magnitude thus the assumptions as given below are validated.
- Flow is entirely laminar, there's no boundary layer release.
- Flow is streamlined, ie, it follows the geometrical path imposed by the curvature.
By D'alembert's paradox, "The net pressure drag exerted on a circular cylinder that moves in an inviscid fluid of large extent is identically zero".Just in the surface of the cylinder, the velocity profile can be given in the next equation:
![V=2Usin\theta](https://tex.z-dn.net/?f=V%3D2Usin%5Ctheta)
And the pressure P on the surface of cylinder is given by Bernoulli's equation along the streamline through that point:
![P=P_{_{\infty }}+\frac{1}{2}\rho U^{2}(1-4sin^{2}\Theta ))](https://tex.z-dn.net/?f=P%3DP_%7B_%7B%5Cinfty%20%7D%7D%2B%5Cfrac%7B1%7D%7B2%7D%5Crho%20U%5E%7B2%7D%281-4sin%5E%7B2%7D%5CTheta%20%29%29)
where P_∞ is Pressure at stagnation point, U is the velocity given, ρ is the density of the fluid (in this case air) and θ is the angle measured from the center of cylinder to the adjacent point where your pressure point will be determine.