Identify the process for which the two integrals ∫Pdv and -∫Vdp, calculated between any two states give the equal value.
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Solution
In isothermal process, temperature remain constant From Ideal gas law, Pv = nRT = constant
Pv = Con differentiating, Pdv + VdP = 0
Pdv = – Vdp
On integrating, ∫Pdv=∫VdP
P∫dv=-V∫dP
If the earliest starting time for an activity is 8 weeks the latest finish time is 37 weeks and the duration time of the activity is 11 weeks, then the total float will be equal to______.
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Solution
Given:Earliest starting time (TE) =8 weeks
Latest finish time (TF) =37 weeks
Duration time (TD) =11 weeks,Then, the total float=TF– TD– TE
=37 –11– 8
=37 –19 =18 weeks
Bottom gating system is sometimes preferred in casting because
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Solution
In bottom gating design, molten metal fills at a faster rate the bottom portion (drag) of mould cavity which rises steadily. As compared with top gating design,bottom gating design includes little turbulence, sand erosion, reduced splashes and better casting surfaces.
Match List I with List II
List I List II
A.Epicyclic gear train. 1.Reducer end thrust.
B.Bevel gear 2.Low gear ratio.
C.Worm and worm gear. 3.Non-parallel,non-intersecting shafts.
D.Herring bone gear. 4.Non-parallel,intersecting shafts.
5.Carrier connects at the center of two gears
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Solution
Epicyclic gear train =carrier connects the center of two gears
Bevel gear = Non-parallel, intersecting shafts.
Worm and worm gear = Non-parallel, Non-intersecting shafts.
Herring bones gear = Reducer end thrust.
The relationship between the shear angle f, the friction angle b and cutting rake angle a is given as :
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Solution
According to Merchant’s theory,
\(\phi =\frac{\pi }{4}-\frac{1}{2}(\beta -\alpha )\)
φ+\(\frac{(\beta -\alpha )}{2}=\frac{\pi }{4}\Rightarrow 2\alpha +\beta -\alpha =\frac{\pi }{4}= constant (c)\)
In a single server queing model if arrival rate is λ and service rate is μ, then the probability of system being idle is:
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Solution
Given : Probability of accomplishing the work (Pa)
\(\frac{Arrival\, rate(\lambda )}{Service\, rate(\mu )}=\frac{\lambda }{\mu }\)
then, probability of being idle(Pi) = 1–Pa
=1-λ⁄μ
With increasing cutting velocity, the total time for machining a component:
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Solution
If cutting velocity is increased, then the total time form a chining a component will decreases.Total machining time (T) = Idle time +cutting time +tool change time.
where, cutting time =\(\frac{\pi \times length\times diameter}{feed\, rate\times cutting\, speed}\)
In the formulation of Lewis equation for toothed gearing, the assumption is made that tangential tooth force (Ft) acts on the:
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Solution
The Lewis equation is derived based on the assumption that tooth is a simple cantilever and tooth contact occurs at the tip of tooth.
Magnus effect can be simulated as a combination of :
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Solution
Magnus effect is an effect in which a spinning object make a curve away from its main path of flight. Magnus effect can be simulated as a combination of uniform flow,irrotational vortex and doublet.
A refrigerator works on reversed carnot cycle producing a temperature of – 40°C. Work done per TR is 700 kJ per 10 min.The value of its CoP will be _____.
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Solution
Given : Work done = 700 kJ/10min.
=\(\frac{700}{10\times 60}\)kJ/S = 7/6 kJ/S= 1.17kJ/S
In case of revered carnot cycle, ITR = 3.52 kw
Now, (CoP) for reversed carnot cycle =\(\frac{3.52}{1.17}\)=3.008