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Q48

REVIEWMCQpage 25holdmath reviewREVIEW_MATH_COMPLEXP2UNREVIEWED

type=MCQ · page=25–26 · marks=2 · content_conf=0.7999999999999999 · math_conf=0.835

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Source / evidence

file: GATE CH 2020 (with Solutions).pdf

pages: 25–26

assets/solutions/Q048/residual_e3c2715e68f5.png

Extracted48 / 67

A student performs a flow experiment with Bingham plastic under fully developed laminar flow conditions in a tube of radius 0.01 m with a pressure drop ( ΔP) of 10 kPa over tube length ( L) of 1.0 m . The velocity profile is flat for r<r_c and parabolic for r≥r_c, as shown in the figure.

r

xr_C Consider r and x as the radial and axial directions, and the shear stress is finite as r approaches zero. A force balance results in the following equation

.

Where τᵣₓ is the shear stress. If r_c is 0.001 m , then the magnitude of yield stress for this Bingham Plastic (in Pa) is

Options

A.
1
B.
5
C.
8
D.
12

Answer

Solution

d(/drr/tau{}_{rx}) = /frac{r(−/Delta{}p)}{L}

[VISUAL / REVIEW — NO INVENTED LATEX] Source math clip

.

r = 0,\tau{}ᵣₓ=0,C=0

.

Hence, the correct option is (B).

Why review

Category: REVIEW_MATH_COMPLEX · Priority: P2 · Disposition: legitimate_uncertain

Complex layout math with partial LaTeX still marked REVIEW_REQUIRED.

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Math review evidence

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Source clip

page=25 bbox=[72,117.16,229.68,132.54]

asset=assets/solutions/Q048/residual_e3c2715e68f5.png

Raw text

rτ= −∂p/Lr²/)2+C

Current normalized

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method=text_first_visual_fallback

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status=REVIEW

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Reason for review: Complex layout math with partial LaTeX still marked REVIEW_REQUIRED.

solution · REVIEW_REQUIRED · visual_fallback

Source clip

page=25 bbox=[72,117.16,229.68,132.54]

asset=assets/solutions/Q048/residual_e3c2715e68f5.png

Raw text

rx(

Current normalized

[VISUAL / REVIEW — NO INVENTED LATEX]

method=text_first_visual_fallback

Resolver / candidate

[VISUAL / REVIEW — NO INVENTED LATEX]

status=REVIEW

reason=fraction_bar_ambiguous

Reason for review: Complex layout math with partial LaTeX still marked REVIEW_REQUIRED.

Provenance status

Source PDF: GATE CH 2020 (with Solutions).pdf

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stem	25	`—`	`—`none	`—`	`REVIEW`
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solution	25	`[72,117.16,229.68,132.54]`	`assets/solutions/Q048/residual_e3c2715e68f5.png`	`—`	`PASS`
solution	25	`[72,117.16,229.68,132.54]`	`assets/solutions/Q048/residual_e3c2715e68f5.png`	`—`	`PASS`
solution	25	`—`	`—`none	`—`	`REVIEW`
solution	25	`—`	`—`none	`—`	`REVIEW`
solution	25	`—`	`—`none	`—`	`REVIEW`

Equations:none

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optionsPASS
answerPASS
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mathREVIEW
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