The location of centre of pressure, which defines the point of application of the total pressure force on the surface, can be calculated by applying the principle of moments according to which "sum of the moment of the resultant force about an axis is equal to the sum of the components about the same axis". The centre of pressure of a rectangular surface (of width 'w') immersed vertically in a static mass of fluid is at a depth of(where, y = depth of the liquid)

The location of centre of pressure, which defines the point of application of the total pressure force on the surface, can be calculated by applying the principle of moments according to which "sum of the moment of the resultant force about an axis is equal to the sum of the components about the same axis". The centre of pressure of a rectangular surface (of width 'w') immersed vertically in a static mass of fluid is at a depth of (where, y = depth of the liquid)

A

$$\frac{1}{{3{\text{y}}}}$$

B

$$\frac{{2{\text{y}}}}{3}$$

C

$$\frac{1}{{4{\text{y}}}}$$

D

$$\frac{{3{\text{y}}}}{4}$$

The depth of centre of pressure (h) for a vertically immersed surface from the liquid surface is given by (where IG = Moment of inertia of the immersed surface about horizontal axis through its centre of gravity, A = Area of immersed surface, and x = Depth of centre of gravity of the immersed surface from the liquid surface)

A

(IG/Ax̅) - x̅

B

(IG/x̅) - Ax̅

C

(Ax̅/IG) + x̅

D

(IG/Ax̅) + x̅

The depth of centre of pressure (h) for a vertically immersed surface from the liquid surface is given by (where $${I_{\text{G}}}$$ = Moment of inertia of the immersed surface about horizontal axis through its centre of gravity, A = Area of immersed surface and x = Depth of centre of gravity of the immersed surface from the liquid surface)

A

$$\frac{{{I_{\text{G}}}}}{{{\text{A}}\overline {\text{x}} }} - \overline {\text{x}} $$

B

$$\frac{{{I_{\text{G}}}}}{{\overline {\text{x}} }} - {\text{A}}\overline {\text{x}} $$

C

$$\frac{{{\text{A}}\overline {\text{x}} }}{{{I_{\text{G}}}}} + \overline {\text{x}} $$

D

$$\frac{{{I_{\text{G}}}}}{{{\text{A}}\overline {\text{x}} }} + \overline {\text{x}} $$

A vertically immersed surface is shown in the below figure. The distance of its centre of pressure from the water surface is
Hydraulics and Fluid Mechanics in ME mcq question image

Hydraulics and Fluid Mechanics in ME mcq question image

A

$$\frac{{{\text{b}}{{\text{d}}^2}}}{{12}} + \overline {\text{x}} $$

B

$$\frac{{{{\text{d}}^2}}}{{12\overline {\text{x}} }} + \overline {\text{x}} $$

C

$$\frac{{{{\text{b}}^2}}}{{12}} + \overline {\text{x}} $$

D

$$\frac{{{{\text{d}}^2}}}{{12}} + \overline {\text{x}} $$

The total pressure on a horizontally immersed surface is (where w = Specific weight of the liquid, A = Area of the immersed surface, and x = Depth of the centre of gravity of the immersed surface from the liquid surface)

A

wA

B

wx

C

wAx

D

wA/x

The total pressure on a horizontally immersed surface is (where w = Specific weight of the liquid, A = Area of the immersed surface and x = Depth of the centre of gravity of the immersed surface from the liquid surface)

A

wA

B

wx

C

wAx

D

$$\frac{{{\text{wA}}}}{{\text{x}}}$$

How far is point 'R' from Point 'T'? Statement (I): Point 'R' is 5 metres to the north of point 'M'. Point 'U' is 4 metres to the east of point 'R'. Point 'T' is to the west of point 'R' such that points 'U' 'R' and 'T' form a straight line of metres. Statement (II): Point 'Z' is metres to the south of point 'T'. Point 'U' is metres to the east of point 'T'. Point 'M' is metres to the east of point 'Z'. Point 'R' is metres to the north of point 'M'. Point 'R' lies on the line formed by joining points 'T' and 'U'.

A

Statement (I) and (III) are independently sufficient to answer the question.

B

Statement (I) and (II) are together required to answer the question.

C

Statement (I) alone is sufficient to answer the question while statement (II) is not sufficient to answer the question.

D

Statement (II) alone is sufficient to answer (I) is not sufficient to answer the question.

Point A is 3m in the north of point B. Point D is 2m in the east of point E. Point F is 9m in the west of point G. Point C is 4m in the west of point B. Point C is 3m in the south of point D. Point F is 5m in the south of point E. Point H is 5m in the north of point G. What is the shortest distance between point H and point A?

A

5m

B

4m

C

3m

D

6m

Point P is 4m in the west of point V. Point R is 6m in the north of point Q. Point T is 5m in the south of point S. Point V is in the middle of point R and Q. Point U is 5m in the east of point R. Point V is in north of point Q. Point S is 5m in the east of point V. What is the area of triangle formed by point P, R and Q?

A

14m²

B

15m²

C

16m²

D

12m²

Study the following information and answer the questions. Point A is 8m to the west of Point B. Point C is 4m to the south of Point B. Point D is 4m to the east of Point C. Point F is 6m to the north of Point D. Point E is 8m to the west of Point F. Point G is 2m to the south of Point E. How far and in which direction is Point G from Point A?

A

4m to the east

B

8m to the west

C

4m to the west

D

8m to the east

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