Answer:
β =
= 0.7071 ≈ 1 ( damping condition )
closed-form expression for the response is attached below
Explanation:
Given : x + 2x + 2x = 0 for Xo = 0 mm and Vo = 1 mm/s
computing a solution :
M = 1,
c = 2,
k = 2,
Wn =
=
next we determine the damping condition using the damping formula
β =
= 0.7071 ≈ 1
from the condition above it can be said that the damping condition indicates underdamping
attached below is the closed form expression for the response
Answer:
The entropy change of the air is ![0.240kJ/kgK](https://tex.z-dn.net/?f=0.240kJ%2FkgK)
Explanation:
![T_{1} =427+273K,T_{1} =700K\\P_{1} =600kPa\\P_{2} =100kPa](https://tex.z-dn.net/?f=T_%7B1%7D%20%3D427%2B273K%2CT_%7B1%7D%20%3D700K%5C%5CP_%7B1%7D%20%3D600kPa%5C%5CP_%7B2%7D%20%3D100kPa)
is unknown
we can apply the following expression to find ![T_{2}](https://tex.z-dn.net/?f=T_%7B2%7D)
![-w_{out} =mc_{v} (T_{2} -T_{1} )](https://tex.z-dn.net/?f=-w_%7Bout%7D%20%3Dmc_%7Bv%7D%20%28T_%7B2%7D%20-T_%7B1%7D%20%29)
![T_{2} =T_{1} -\frac{w_{out } }{mc_{v} }](https://tex.z-dn.net/?f=T_%7B2%7D%20%3DT_%7B1%7D%20-%5Cfrac%7Bw_%7Bout%20%7D%20%7D%7Bmc_%7Bv%7D%20%7D)
now substitute
![T_{2} =700K-\frac{600kJ}{5kg*0.718kJ/kgK} \\T_{2}=533K](https://tex.z-dn.net/?f=T_%7B2%7D%20%3D700K-%5Cfrac%7B600kJ%7D%7B5kg%2A0.718kJ%2FkgK%7D%20%5C%5CT_%7B2%7D%3D533K)
To find entropy change of the air we can apply the ideal gas relationship
Δ![s_{air}](https://tex.z-dn.net/?f=s_%7Bair%7D)
![=c_{p} ln\frac{T_{2} }{T_{1} } -Rln\frac{P_{2} }{P_{1} }](https://tex.z-dn.net/?f=%3Dc_%7Bp%7D%20ln%5Cfrac%7BT_%7B2%7D%20%7D%7BT_%7B1%7D%20%7D%20-Rln%5Cfrac%7BP_%7B2%7D%20%7D%7BP_%7B1%7D%20%7D)
Δ![s_{air} =](https://tex.z-dn.net/?f=s_%7Bair%7D%20%3D)
![1.005*ln(\frac{533}{700})-0.287* in(\frac{100}{600} )](https://tex.z-dn.net/?f=1.005%2Aln%28%5Cfrac%7B533%7D%7B700%7D%29-0.287%2A%20in%28%5Cfrac%7B100%7D%7B600%7D%20%29)
Δ![s_{air} =0.240kJ/kgK](https://tex.z-dn.net/?f=s_%7Bair%7D%20%3D0.240kJ%2FkgK)
Answer: Option D, piezoelectric pressure guage
Explanation: Quartz crystal possess a very useful quality in science as they can generate small charges when pressure is applied to them or when they are hit. This property can be harnessed to construct a piezoelectric pressure gauge which would be used to measure and indicate changes in pressure, the quartz crystal releases little voltage each time there is an applied pressure . This device would be able to sense changes in pressure as there would voltage proportional to the applied pressure.
Answer:
power developed by the turbine = 6927.415 kW
Explanation:
given data
pressure = 4 MPa
specific enthalpy h1 = 3015.4 kJ/kg
velocity v1 = 10 m/s
pressure = 0.07 MPa
specific enthalpy h2 = 2431.7 kJ/kg
velocity v2 = 90 m/s
mass flow rate = 11.95 kg/s
solution
we apply here thermodynamic equation that
energy equation that is
![h1 + \frac{v1}{2} + q = h2 + \frac{v2}{2} + w](https://tex.z-dn.net/?f=h1%20%2B%20%5Cfrac%7Bv1%7D%7B2%7D%20%20%2B%20q%20%3D%20h2%20%2B%20%5Cfrac%7Bv2%7D%7B2%7D%20%20%2B%20w)
put here value with
turbine is insulated so q = 0
so here
![3015.4 *1000 + \frac{10^2}{2} = 2431.7 * 1000 + \frac{90^2}{2} + w](https://tex.z-dn.net/?f=3015.4%20%2A1000%20%2B%20%5Cfrac%7B10%5E2%7D%7B2%7D%20%20%3D%20%202431.7%20%2A%201000%20%2B%20%5Cfrac%7B90%5E2%7D%7B2%7D%20%20%2B%20w)
solve we get
w = 579700 J/kg = 579.7 kJ/kg
and
W = mass flow rate × w
W = 11.95 × 579.7
W = 6927.415 kW
power developed by the turbine = 6927.415 kW
Answer:
Spindle
Explanation:
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