16. A single pipe of length 1500 m and diameter 60 cm connects two reservoirs having a difference of 20 m in their water levels. The pipe is to be replaced by two pipes of the same length and equal diameter d to convey 25% more discharge under the same head loss. If the friction factor is assumed to be the same for all the pipes, the value of d is approximately equal to which of the following options?
    

1. 1. 37.5 cm

   
   
   

   2. 40.0 cm

   
   
   

   3. 45.0 cm

   
   
   

   4. 50.0 cm

   
   
   

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1. View Hint View Answer Discuss in Forum

   Total discharge = 1.25 × Q
   

   Discharge in one pipe =	1.25Q
   	2

   
   

   Head loss in one pipe, hf1 =	flV²
   	2gD1

   
   

   =	flQ¹2
   	2gD1A²

   
   

   =	fl.(125Q / 2)²
   	2gD1 × (D1²)²

   
   Initial head loss, h_f1 = final head loss, h_f2
   
   ∴ D₁ = 50 cm.

   Correct Option: D

   Total discharge = 1.25 × Q
   

   Discharge in one pipe =	1.25Q
   	2

   
   

   Head loss in one pipe, hf1 =	flV²
   	2gD1

   
   

   =	flQ¹2
   	2gD1A²

   
   

   =	fl.(125Q / 2)²
   	2gD1 × (D1²)²

   
   Initial head loss, h_f1 = final head loss, h_f2
   
   ∴ D₁ = 50 cm.

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17. The relation that must hold for the flow to be irrotational is

1. 1. ∂u	−	∂v	= 0
      ∂y		∂x

   
   
   

   2. ∂u	=	∂v
      ∂x		∂y

   
   
   

   3. ∂²u	+	∂²v	= 0
      ∂x²		∂y²

   
   
   

   4. ∂u	= −	∂v
      ∂y		∂x

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let us consider a steady two dimensional flow of an ideal fluid in a rectangular cartesian coordinate system. The velocity field is given by,
   V = i^→ u t j^→ v
   Hence the condition of irrotationality is
   
   

   ⇒	∂v	−	∂u	= 0
   	∂x		∂y

   Correct Option: A

   Let us consider a steady two dimensional flow of an ideal fluid in a rectangular cartesian coordinate system. The velocity field is given by,
   V = i^→ u t j^→ v
   Hence the condition of irrotationality is
   
   

   ⇒	∂v	−	∂u	= 0
   	∂x		∂y

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18. In a Bernoulli equation, used in pipe flow, each term represents

1. 1. Energy per unit weight

   
   
   

   2. Energy per unit mass

   
   
   

   3. Energy per unit volume

   
   
   

   4. Energy per unit flow length

   
   
   

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1. View Hint View Answer Discuss in Forum

   Bernoullis equation is,
   

   P	+	V²	+ Z = 0
   ρg		2g

   
   

   Where,	P	is pressure head
   	ρg

   
   

   V²	is kinetic head
   2g

   
   Z is potential head
   Each term represents energy per unit weight

   Correct Option: A

   Bernoullis equation is,
   

   P	+	V²	+ Z = 0
   ρg		2g

   
   

   Where,	P	is pressure head
   	ρg

   
   

   V²	is kinetic head
   2g

   
   Z is potential head
   Each term represents energy per unit weight

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19. For a pipe of radius, r, flowing half full under the action of gravity, the hydraulic depth is

1. 1. r

   
   
   

   2. πr

      4

   
   
   

   3. r

      2

   
   
   

   4. 0379 r

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   Top width, T = r + r = 2r
   

   Hydraulic depth, D =	A
   	T

   
   

   =	(πr²)/2
   	2r

   
   

   =	πr
   	4

   Correct Option: B

   
   Top width, T = r + r = 2r
   

   Hydraulic depth, D =	A
   	T

   
   

   =	(πr²)/2
   	2r

   
   

   =	πr
   	4

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20. A steady flow occurs in an open channel with lateral inflow of q m³ /s per unit width as shown in the figure. The mass conservation equation is
    

1. 1. ∂q	= 0
      ∂x

   
   
   

   2. ∂Q	= 0
      ∂x

   
   
   

   3. ∂Q	− q = 0
      ∂x

   
   
   

   4. ∂Q	+ pq = 0
      ∂x

   
   
   

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1. View Hint View Answer Discuss in Forum

   Mass concentration equation is the continuity equation.
   
   In a distance ∂x, change in dischargein ∂Q
   

   ∴	∂Q	= q
   	∂x

   
   

   ∴	∂Q	− q = 0
   	∂x

   Correct Option: C

   Mass concentration equation is the continuity equation.
   
   In a distance ∂x, change in dischargein ∂Q
   

   ∴	∂Q	= q
   	∂x

   
   

   ∴	∂Q	− q = 0
   	∂x

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