26. A river reach of 2.0 km long with maximum flood discharge of 10000 m³ /s is to be physically modeled in the laboratory where maximum available discharge is 0.20 m³ /s. For a geometrically similar model based on equality of Froude number, the length of the river reach (m) in the model is
    

1. 1. 26.4

   
   
   

   2. 25.0

   
   
   

   3. 20.5

   
   
   

   4. 18.0

   
   
   

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1. View Hint View Answer Discuss in Forum

   Fr =	V
   	√gy

   
   

   	Vm	=	Vp
   	√g ym		√g yp

   
   ∴ V_r = √L_r
   Q_r = A_r V_r
   = A × L_r²
   = √L_r × L_r² = (L_r)^{5 / 2}
   ∴ L_r = (Q_r)^{2 / 5}
   

   =		0.2		2 / 5	= 0.0131
   		104

   
   

   	Lm	= Lr
   	Lp

   
   L_m = L_r × L_p
   = 0.0131 × 2000 = 26.4 m.

   Correct Option: A

   Fr =	V
   	√gy

   
   

   	Vm	=	Vp
   	√g ym		√g yp

   
   ∴ V_r = √L_r
   Q_r = A_r V_r
   = A × L_r²
   = √L_r × L_r² = (L_r)^{5 / 2}
   ∴ L_r = (Q_r)^{2 / 5}
   

   =		0.2		2 / 5	= 0.0131
   		104

   
   

   	Lm	= Lr
   	Lp

   
   L_m = L_r × L_p
   = 0.0131 × 2000 = 26.4 m.

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27. The channel width is to be contracted. The minimum width to which the channel can be contracted without affecting the upstream flow condition is
    

1. 1. 3.0 m

   
   
   

   2. 3.8 m

   
   
   

   3. 4.1 m

   
   
   

   4. 4.5 m

   
   
   

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1. View Hint View Answer Discuss in Forum

   When width is contracted, the depth decreases to critical depth, i.e. flow is critical means minimum specific energy.
   

   Emin =	3	yc
   	2

   
   

   1.74 =	3	×		q2		1 / 3
   	2			g

   
   
   ∴ B = 4.1 m.

   Correct Option: C

   When width is contracted, the depth decreases to critical depth, i.e. flow is critical means minimum specific energy.
   

   Emin =	3	yc
   	2

   
   

   1.74 =	3	×		q2		1 / 3
   	2			g

   
   
   ∴ B = 4.1 m.

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28. The depth of flow in an alluvial channel is 1.5 m. If critical velocity ratio is 1.1 and Manning’s ‘n’ is 0.018, the critical velocity of the channel as per Kennedy’s method is
    

1. 1. 0.713 m/s

   
   
   

   2. 0.784 m/s

   
   
   

   3. 0.879 m/s

   
   
   

   4. 1.108 m/s

   
   
   

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   NA

   Correct Option: B

   NA

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29. Water flows through a 100 mm diameter pipe with a velocity of 0.015 m/sec. If the kinematic viscosity of water is 1.13 × 10^–6 m² /sec, the friction factor of the pipe material is
    

1. 1. 0.0015

   
   
   

   2. 0.032

   
   
   

   3. 0.037

   
   
   

   4. 0.048

   
   
   

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1. View Hint View Answer Discuss in Forum

   Re =	0.015 × 0.1	= 1327 (< 2000)
   	1.13 × 10-6

   
   ∴ It is laminar flow. (Re < 2000)
   

   Friction factor, f =	64	= 0.048
   	Re

   
   

   Correct Option: D

   Re =	0.015 × 0.1	= 1327 (< 2000)
   	1.13 × 10-6

   
   ∴ It is laminar flow. (Re < 2000)
   

   Friction factor, f =	64	= 0.048
   	Re

   
   

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30. A rectangular open channel of width 4.5 m is carrying a discharge of 100 m³ /sec. The critical depth of the channel is
    

1. 1. 7.09 m

   
   
   

   2. 3.69 m

   
   
   

   3. 2.16 m

   
   
   

   4. 1.31 m

   
   
   

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1. View Hint View Answer Discuss in Forum

   yc =		q²		1/3
   		g

   
   

   q =	Q	=	100	22.2m³/s
   	B		4.5

   
   

   ∴ yc =		22.2²		1/3	= 3.69 m.
   		9.81

   Correct Option: B

   yc =		q²		1/3
   		g

   
   

   q =	Q	=	100	22.2m³/s
   	B		4.5

   
   

   ∴ yc =		22.2²		1/3	= 3.69 m.
   		9.81

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