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)

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

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

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

Consider a given volume of liquid at a temperature T below Tm with a free energy G’. If some of the atoms of the liquid cluster together to form a small sphere of solid, the free energy of the system will change to G, given by________ (Assume V1 volume of the solid sphere, V2 volume of liquid, A is the solid/liquid interfacial area, γ solid/liquid interface free energy, G1 and G2 are the free energies per unit volume of solid and liquid respectively).

A

V1G1 + V2G2 + Aγ

B

V1G2 + V2G1 + Aγ

C

V1G1 + V2G2 – Aγ

D

V1G2 + V2G1 – Aγ

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

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

An internal mouthpiece is said to be running free if the length of the mouthpiece is __________ the diameter of the orifice.

A

Less than twice

B

More than twice

C

Less than three times

D

More than three times

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 coefficient of discharge in case of internal mouthpiece is __________ that of external mouthpiece.

A

Less than

B

More than

C

Equal to

D

None of these

An internal mouthpiece is said to be running __________ if the length of the mouthpiece is more than three times the diameter of the orifice.

A

Free

B

Partially

C

Full

D

None of these

A large tank of height h is filled with a liquid of density ρ. A similar tank is half-filled with this liquid and other-halffilled with another liquid of density 2ρ 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

2 : 3

B

2 : √3

C

√2 : 3

D

√2 : √3

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)

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