The discharge through an external mouthpiece is given by (where a = Cross-sectional area of the mouthpiece, and H = Height of liquid above the mouthpiece)

When an internal mouthpiece is running free, the discharge through the mouthpiece is (where a = Area of mouthpiece, and H = Height of liquid above the mouthpiece)

A

0.5 a. √2gH

B

0.707 a. √2gH

C

0.855 a. √2gH

D

a. √2gH

When an internal mouthpiece is running free, the discharge through the mouthpiece is (where a = Area of mouthpiece and H = Height of liquid above the mouthpiece)

A

$$0.5{\text{a}}\sqrt {2{\text{gH}}} $$

B

$$0.707{\text{a}}\sqrt {2{\text{gH}}} $$

C

$$0.855{\text{a}}\sqrt {2{\text{gH}}} $$

D

$${\text{a}}\sqrt {2{\text{gH}}} $$

The discharge through an external mouthpiece is given by (where a = Cross-sectional area of the mouthpiece and H = Height of liquid above the mouthpiece)

A

$$0.855{\text{a}}\sqrt {2{\text{gH}}} $$

B

$$1.855{\text{aH}}\sqrt {2{\text{g}}} $$

C

$$1.585{\text{a}}\sqrt {2{\text{gH}}} $$

D

$$5.85{\text{aH}}\sqrt {2{\text{g}}} $$

“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 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

Two centrifugal pumps P and R are available for use in a pipe flow system and their head-discharge characteristics are as follows. Pump P Pump R Discharge (cumecs) Head (m) Discharge (cumecs) Head (m) 0 40 0 45 0.12 35 0.14 40 0.2 28 0.24 35 0.3 18 0.3 28 The following statements (S1, S2, and S3) pertain to the head and discharge values during actual operation. Neglect losses in the system. Which of the following statements are correct? S1: When the two pumps P and R are connected in parallel, the discharge is 0.36 cumecs corresponding to a head of 35 m. S2: When the two pumps P and R are connected in parallel, the discharge is 0.36 cumecs corresponding to a head of 70 m. S3: When the two pumps P and R are connected in series, the discharge is 0.3 cumecs corresponding to a head of 46 m.

A

S2 only

B

S1 and S3

C

S1 and S2

D

S2 and S3

The discharge through a convergent mouthpiece is __________ the discharge through an internal mouthpiece of the same diameter and head of water.

A

Equal to

B

One-half

C

Three fourth

D

Double

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 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

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

In an internal mouthpiece, if the jet after contraction does not touch the sides of the mouthpiece, then the mouthpiece is said to be

A

Running full

B

Running free

C

Partially running full

D

Partially running free

The discharge through an external mouthpiece is given by (where a = Cross-sectional area of the mouthpiece, and H = Height of liquid above the mouthpiece)

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