The discharge through a small rectangular orifice is given by (where Cd = Coefficient of discharge for the orifice, a = Cross-sectional area of the orifice, h = Height of the liquid above the centre of the orifice)

The discharge through a small rectangular orifice is given by (where C_d = Coefficient of discharge for the orifice, a = Cross-sectional area of the orifice, h = Height of the liquid above the centre of the orifice)

A

$${\text{Q}} = {{\text{C}}_{\text{d}}} \times {\text{a}} \times \sqrt {2{\text{gh}}} $$

B

$${\text{Q}} = \frac{2}{3}{{\text{C}}_{\text{d}}} \times {\text{a}} \times {\text{h}}$$

C

$${\text{Q}} = \frac{{{{\text{C}}_{\text{d}}} \times {\text{a}}}}{{\sqrt {2{\text{gh}}} }}$$

D

$${\text{Q}} = \frac{{3{{\text{C}}_{\text{d}}} \times {\text{a}}}}{{\sqrt {2{\text{h}}} }}$$

The discharge through a large rectangular orifice is given by (where H₁ = Height of the liquid above the top of the orifice, H₂ = Height of the liquid above the bottom of the orifice, b = Breadth of the orifice and C_d = Coefficient of discharge)

A

$${\text{Q}} = \frac{2}{3} \times {{\text{C}}_{\text{d}}} \times {\text{b}}\sqrt {2{\text{g}}} \left( {{{\text{H}}_2} - {{\text{H}}_1}} \right)$$

B

$${\text{Q}} = \frac{2}{3} \times {{\text{C}}_{\text{d}}} \times {\text{b}}\sqrt {2{\text{g}}} \left( {{\text{H}}_2^{\frac{1}{2}} - {\text{H}}_1^{\frac{1}{2}}} \right)$$

C

$${\text{Q}} = \frac{2}{3} \times {{\text{C}}_{\text{d}}} \times {\text{b}}\sqrt {2{\text{g}}} \left( {{\text{H}}_2^{\frac{3}{2}} - {\text{H}}_1^{\frac{3}{2}}} \right)$$

D

$${\text{Q}} = \frac{2}{3} \times {{\text{C}}_{\text{d}}} \times {\text{b}}\sqrt {2{\text{g}}} \left( {{\text{H}}_2^2 - {\text{H}}_1^2} \right)$$

The discharge through a wholly drowned orifice is given by (where H₁ = Height of water (on the upstream side) above the top of the orifice, H₂ = Height of water (on the downstream side) above the bottom of the orifice and H = Difference between two water levels on either side of the orifice)

A

$${\text{Q}} = {{\text{C}}_{\text{d}}} \times {\text{b}}{{\text{H}}_1}\sqrt {2{\text{gh}}} $$

B

$${\text{Q}} = {{\text{C}}_{\text{d}}} \times {\text{b}}{{\text{H}}_2}\sqrt {2{\text{gh}}} $$

C

$${\text{Q}} = {{\text{C}}_{\text{d}}} \times {\text{b}}\left( {{{\text{H}}_2} - {{\text{H}}_1}} \right)\sqrt {2{\text{gh}}} $$

D

$${\text{Q}} = {{\text{C}}_{\text{d}}} \times {\text{bH}}\sqrt {2{\text{gh}}} $$

“What is the different between height and radius of solid cylinder?” Which of the following option is sufficient alone to find the answer? A) A solid cylinder is made by melting a solid sphere. The radius of cylinder is 3 times the radius of a circle whose area is 154 sq.m. Height of cylinder is equal to the height of cone whose volume is 2772 cubic meters. B) Area of a rectangle whose longer side is ¾ times the radius of a solid cylinder, is 168 sq.m and, Volume of solid cylinder is 2772 cubic meters and its height is 18 m. C) A metallic cone of radius 15m and height 35m is melted into the solid cylinder of radius equal to the radius of a circle whose area is equal to the area of rectangle whose sides are in the ratio 4 : 3 respectively. D) The curved surface area of the solid cylinder is 3 time the surface area of a sphere of radius 7m and height of cylinder is equal to the height of a metallic cone whose curved surface area is 308 sq.m.

A

Only A and B

B

Only B and C

C

Only B

D

All A, B, C and D

E

None of A, B, C and D

The discharge through fully submerged orifice is - Where, H = Difference in level of water H1 = Height of water above the top of the orifice on the upstream side H2 = Height of water above the bottom of the orifice

A

${c_d} \times b \times \left( {{H_2} - {H_1}} \right) \times \sqrt {2gH} $

B

${c_d} \times b \times \left( {\;H_2^{\frac{3}{2}} - H_1^{\frac{3}{2}}} \right) \times \sqrt {2gH} $

C

None of these

D

${c_d} \times b \times \left( {\;{H_2} - {H_1}} \right) \times \sqrt {2g} \times {H^{\frac{3}{2}}}$

A rectangular orifice of 2 m width and 1.2 m deep is fitted in one side of large tank. The easier level on one side of the orifice is 3m above the top edge of the orifice while on the other side of the orifice the water level is 0.5 m below it’s top edge. Calculate discharge if Cd = .64

A

4.95 m3/s

B

5.67 m3/s

C

3.56 m3/s

D

6.75 m3/s

Some small cubes of same height 7 cm but variable length and width are put inside a large cuboid of height 21 cm. Length and width of cuboid is 32 cm and 24 cm, respectively. Small cubes are put such that cubes at the bottom most layer is of similar base area; second layer contains all the cubes of similar base area and third layer have all the cubes of similar base area. Which of the following statement(s) given below is / are TRUE? A: If side of each small cubes at bottom most layer is 8 cm, then maximum number of small cubes that can be put at bottom most layer is 12. B: If maximum of 48 cubes can be put at second layer, then side of each cube at second layer is 6 cm. C: If side of each small cubes at third layer is 1.6 cm, then maximum number of small cubes that can be put at third layer is 300.

A

C

B

A and B

C

A and C

D

B and C

A large tank of height h is half-filled with a liquid of density ρ and other half-filled with a liquid of density 4ρ. A similar tank is half-filled with a liquid of density 2ρ and other-half filled with another liquid of density 3ρ as shown. What will be the ratio of the instantaneous velocities of discharge through a small opening at the base of the tanks? (assume that the diameter of the opening is negligible compared to the height of the liquid column in either of the tanks)

A

1 : 1

B

1 : 2

C

2 : 1

D

1 : 3

The following question, there are three statements I, II and III. Read the question carefully and mark your answer according to which statements(s) is/are sufficient to the answer the question. What proportion of liquid of type C is there in the tank of capacity 60 liters after 2 minutes if the tank is initially empty? Statement I: Three pipes P, Q, R fill the tank in 15 minutes, 12 minutes and 10 minutes respectively Statement II: When the tank was empty all the three pipes are opened and they discharge three different types of liquid Statement III: Pipe P discharge type A liquid, pipe Q discharge type B liquid and Pipe R discharge type C liquid

A

Only III

B

I and III together

C

All I, II and III

D

Data insufficient

E

None of these

A fluid flows through an orifice of an area 0.4 m2 with an actual discharge of 400 l/s. If the theoretical velocity of flow through the orifice is 2 m/s, what is the coefficient of discharge?

A

0.71

B

0.68

C

0.50

D

0.56

The discharge through a small rectangular orifice is given by (where Cd = Coefficient of discharge for the orifice, a = Cross-sectional area of the orifice, h = Height of the liquid above the centre of the orifice)

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