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ohaa [14]
3 years ago
14

What are the units or dimensions of the shear rate dv/dy (English units)? Then, what are the dimensions of the shear stress τ= μ

*dV/dy? Then, by dimensional analysis, show that the shear stress has the same units as momentum divided by (area*time).What are the unit or dimensions of viscosity?
Engineering
1 answer:
swat323 years ago
4 0

Answer:

1) Dimensions of shear rate is [T^{-1}] .

2)Dimensions of shear stress are [ML^{-1}T^{-2}]

Explanation:

Since the dimensions of velocity 'v' are [LT^{-1}] and the dimensions of distance 'y'  are [L] , thus the dimensions of \frac{dv}{dy} become

\frac{[LT^{-1}]}{[L]}=[T^{-1}] and hence the units become s^{-1}.

Now we know that the dimensions of coefficient of dynamic viscosity \mu are [ML^{-1}T^{-1}] thus the dimensions of shear stress can be obtained from the given formula as

[\tau ]=[ML^{-1}T^{-1}]\times [T^{-1}]\\\\[\tau ]=[ML^{-1}T^{-2}]

Now we know that dimensions of momentum are [MLT^{-1}]

The dimensions of Area\times time are [L^{2}T]

Thus the dimensions of \frac{Moumentum}{Area\times time}=\frac{MLT^{-1}}{L^{2}T}=[MLT^{-2}]

Which is same as that of shear stress. Hence proved.

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Mahamad Siddiqui sent false emails and letters of recommendation on behalf of individuals without their permission to nominate h
shusha [124]

Mahamad Siddiqui sent false emails and letters of recommendation on behalf of individuals without their permission to nominate himself for the Waterman Award at the National Science Foundation. His earlier emails were offered where he had solicited letters were offered as evidence. Siddiqui claimed that content of earlier emails was hearsay. Do the earlier emails come in is given below

Explanation:

1.Mohamed Siddiqui appeals his convictions for fraud and false statements to a federal agency, and obstruction in connection with a federal investigation.   Siddiqui challenges the district court's admission into evidence of e-mail and foreign depositions.

2.On February 18, 1997, Jodi Saltzman, a special agent with the NSF interviewed Siddiqui at Siddiqui's office at the University of South Alabama.   During the interview, Siddiqui signed a statement admitting that he had nominated himself for the Waterman Award, but that he had permission from Yamada and von Gunten to submit forms on their behalf.   Siddiqui also acknowledged in the statement that Westrick had recommended Siddiqui for a different award, the PECASE Award, but that Siddiqui had changed the wording of the letter to apply to the Waterman Award.   Siddiqui was indicted on April 29, 1997.

3.Siddiqui opposed the taking of the depositions on the grounds that the witnesses' personal presence at trial was necessary, and that Indian travel restrictions for its citizens residing abroad prevented him from traveling to Japan and Switzerland.   Specifically, Siddiqui asserted that because of religious persecution in India his travel to Japan or Switzerland related to the criminal action would put his family members still living in India at risk.   The magistrate judge ruled that the government had carried its burden of showing that Yamada and von Gunten would be unavailable to appear at trial, and instructed that Siddiqui's fear of obtaining a travel visa from India because of the threat of persecution of family members should not preclude the taking of the foreign depositions.

4.Yamada's deposition was taken in Japan on March 6, 1998.   At government expense, Siddiqui's counsel attended the deposition and cross-examined the witness, but was not in telephonic contact with Siddiqui during the deposition.   Yamada testified that on February 1, 1997, she received an e-mail stating that if she received a phone call from the NSF to “please tell good words about me.”   Yamada testified that she knew the e-mail was from Siddiqui because the name on the e-mail had Siddiqui's sender address, and it ended with the name “Mo” which Siddiqui had previously told her was his nickname, and which he had used in previous e-mail.

5.Yamada later admitted to Saltzman that she had not given Siddiqui permission to sign, but had made the earlier representation because she thought Siddiqui would go to jail.

6.During cross-examination of Yamada at the deposition, Siddiqui's counsel introduced an e-mail from Yamada to Siddiqui.   This e-mail contained the same e-mail address for Siddiqui as the e-mail received by Yamada and von Gunten apparently from Siddiqui.

7.Von Gunten's video deposition was taken in Switzerland.   At government expense, Siddiqui's counsel attended the deposition and cross-examined von Gunten.   During the deposition, Siddiqui was in communication with his counsel by telephone.   Von Gunten testified at the deposition that he had not submitted a letter of recommendation in favor of Siddiqui for the Waterman Award, and that he had not given Siddiqui permission to submit such a letter in his name.

8 0
4 years ago
A fluid of density 900 kg/m3 passes through a converging section of an upstream diameter of 50 mm and a downstream diameter of 2
NISA [10]

Answer:

Q= 4.6 × 10⁻³ m³/s

actual velocity will be equal to 8.39 m/s

Explanation:

density of fluid = 900 kg/m³

d₁ = 0.025 m

d₂ = 0.05 m

Δ P = -40 k N/m²

C v = 0.89

using energy equation

\dfrac{P_1}{\gamma}+\dfrac{v_1^2}{2g} = \dfrac{P_2}{\gamma}+\dfrac{v_2^2}{2g}\\\dfrac{P_1-P_2}{\gamma}=\dfrac{v_2^2-v_1^2}{2g}\\\dfrac{-40\times 10^3\times 2}{900}=v_2^2-v_1^2

under ideal condition v₁² = 0

v₂² = 88.88

v₂ = 9.43 m/s

hence discharge at downstream will be

Q = Av

Q = \dfrac{\pi}{4}d_1^2 \times v

Q = \dfrac{\pi}{4}0.025^2 \times 9.43

Q= 4.6 × 10⁻³ m³/s

we know that

C_v =\dfrac{actual\ velocity}{theoretical\ velocity }\\0.89 =\dfrac{actual\ velocity}{9.43}\\actual\ velocity = 8.39m/s

hence , actual velocity will be equal to 8.39 m/s

6 0
3 years ago
stimate the maximum efficiency of an automobile engine that has a compression ratio of 5:1.0. Assume the engine operates accordi
Fed [463]

Answer:

Efficiency based on Otto cycle.

Effotto = 47.47%

Explanation:

Efficiency based on Otto cycle.

effotto = 1 – (V2 / V1)^γ-1

effotto = 1 – (1 / 5)^1.4 - 1

effotto = 47.47%

5 0
3 years ago
why is the peak value of the rectified output less than the peak value of the ac input and by how much g
Bumek [7]

Answer:

The Peak value of the output voltage is less or lower than that of the peak value of the input voltage by 0.6V reason been that the voltage is tend to drop across the diode.

Explanation:

This is what we called HALF WAVE RECTIFIER in which the Peak value of the output voltage is less or lower than that of the peak value of the input voltage by 0.6V reason been that the voltage is tend to drop across the diode.

Therefore this is the formula for Half wave rectifier

Vrms = Vm/2 and Vdc

= Vm/π:

Where,

Vrms = rms value of input

Vdc = Average value of input

Vm = peak value of output

Hence, half wave rectifier is a rectifier which allows one half-cycle of an AC voltage waveform to pass which inturn block the other half-cycle which is why this type of rectifiers are often been used to help convert AC voltage to a DC voltage, because they only require a single diode to inorder to construct.

5 0
3 years ago
Consider a flat plate that is 25 mm long, 30 mm wide, and 1 mm thick and a 50 mm long cylinder with the same volume as the plate
Blizzard [7]

Answer:

Average heat transfer =42.448w/m^2k

Nud = 13.45978

Explanation:

See attachment for step by step guide

4 0
3 years ago
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