The discharge over a right angled notch is (where H = Height of liquid above the apex of notch)

The discharge over the trapezoidal notch is equal to the discharge over the rectangular notch __________ the discharge over the triangular notch.

A

Plus

B

Minus

C

Divide

D

None of these

The discharge over a rectangular notch is (where b = Width of notch, and H = Height of liquid, above the sill of the notch)

A

(2/3) Cd × b × √(2gH)

B

(2/3) Cd × b × √(2g) × H

C

(2/3) Cd × b × √(2g) × H3/2

D

(2/3) Cd × b × √(2g) × H2

The discharge over a rectangular notch is (where b = Width of notch and H = Height of liquid, above the sill of the notch)

A

$$\frac{2}{3}{{\text{C}}_{\text{d}}} \times {\text{b}}\sqrt {2{\text{gH}}} $$

B

$$\frac{2}{3}{{\text{C}}_{\text{d}}} \times {\text{b}}\sqrt {2{\text{g}}} \times {\text{H}}$$

C

$$\frac{2}{3}{{\text{C}}_{\text{d}}} \times {\text{b}}\sqrt {2{\text{g}}} \times {{\text{H}}^{\frac{3}{2}}}$$

D

$$\frac{2}{3}{{\text{C}}_{\text{d}}} \times {\text{b}}\sqrt {2{\text{g}}} \times {{\text{H}}^2}$$

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

An error of 1% in measuring head over the apex of the notch (H) will produce an error of _________ in discharge over a triangular notch.

A

1%

B

1.5%

C

2%

D

2.5%

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

If the coefficient of discharge is 0.6, then the discharge over a right angled notch is

A

$$0.417\,{{\text{H}}^{\frac{5}{2}}}$$

B

$$1.417\,{{\text{H}}^{\frac{5}{2}}}$$

C

$$4.171\,{{\text{H}}^{\frac{5}{2}}}$$

D

$$7.141\,{{\text{H}}^{\frac{5}{2}}}$$

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

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

If a + b + c + d = 4, then find the value of $$\frac{1}{{\left( {1 - a} \right)\left( {1 - b} \right)\left( {1 - c} \right)}}$$ + $$\frac{1}{{\left( {1 - b} \right)\left( {1 - c} \right)\left( {1 - d} \right)}}$$ + $$\frac{1}{{\left( {1 - c} \right)\left( {1 - d} \right)\left( {1 - a} \right)}}$$ + $$\frac{1}{{\left( {1 - d} \right)\left( {1 - a} \right)\left( {1 - b} \right)}}$$ is?

A

0

B

5

C

1

D

4

The discharge over a right angled notch is (where H = Height of liquid above the apex of notch)

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