61. Consider a fully developed steady laminar flow of an in compressible fluid with viscosity μ. through a circular pipe of radius R, Given that the velocity at a radial location of R/2 from the centerline of the pipe is U₁, the shear stress at the wall is KμU₁ /R, where K is _______.

1. 1. 3.21

   
   
   

   2. 5.24

   
   
   

   3. 6.24

   
   
   

   4. None of these

   
   
   

---

1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: D

   NA

---

62. Consider fluid flow between two infinite horizontal plates when are parallel (the gap between them being 50 mm), The top plate is sliding parallel to the stationary bottom plate at a speed of 3 m/s.
    The flow between the plates is solely due to the motion of the top plate. The force per unit area (magnitude) required to maintain the bottom plate stationary is ________ N/m².
    Viscosity of the fluid μ = 0.44 kg/ms and density p = 888 kg/m³.

1. 1. 26.4

   
   
   

   2. 26.9

   
   
   

   3. 26.7

   
   
   

   4. 26.8

   
   
   

---

1. View Hint View Answer Discuss in Forum

   
   

   du	= 7	8.0	= 60
   dy		0.05

   
   

   Shear strees = τ = μ	du
   	dy

   
   = 0.44 × 60 = 26.4 N/m²

   Correct Option: A

   
   

   du	= 7	8.0	= 60
   dy		0.05

   
   

   Shear strees = τ = μ	du
   	dy

   
   = 0.44 × 60 = 26.4 N/m²

---

63. Oil (kinematic viscosity, υ _oil = 1.0 × 10^-6 m²/s) flows through a pipe of 0.5 m diameter with a velocity of 10 m/s. Water (kinematic viscosity, v_w = 0.89 × 10^-6 m²/s) is flowing through a model pipe of diameter 20 mm. For satisfying the dynamic similarity, the velocity of water (in m/s) is _______.

1. 1. 21.24

   
   
   

   2. 23.25

   
   
   

   3. 22.25

   
   
   

   4. 22

   
   
   

---

1. View Hint View Answer Discuss in Forum

   oil water
   v = 1.0 × 10^–5 m²/s v = 0.89 × 10– 6 m²/s
   d = 0.5 m
   d = 0.02 m
   v = 10 m/sec
   v =?
   [R_e]_(oil) = [R_e]_(w)
   

   10 × 0.5	=	V × 0.02
   1.0 × 10-5		8.9 × 10-6

   
   ⇒ v = 22.25 m/s
   

   Correct Option: C

   oil water
   v = 1.0 × 10^–5 m²/s v = 0.89 × 10– 6 m²/s
   d = 0.5 m
   d = 0.02 m
   v = 10 m/sec
   v =?
   [R_e]_(oil) = [R_e]_(w)
   

   10 × 0.5	=	V × 0.02
   1.0 × 10-5		8.9 × 10-6

   
   ⇒ v = 22.25 m/s
   

---

64. For a fully developed laminar flow of water (dynamic viscosity 0.001 Pa-s) through a pipe radius 5 cm, the axial pressure gradient is –10 Pa/m. The magnitude of axial velocity (in m/s) at a radial location of 0.2 cm is ________.

1. 1. 6.24

   
   
   

   2. 6.29

   
   
   

   3. 6.26

   
   
   

   4. 6.34

   
   
   

---

1. View Hint View Answer Discuss in Forum

   u =	-1 δP	(R² - r²)
   	4μδx

   
   

   =	-1	× (-10)((0.05)² - (0.002)²)
   	4μδx

   
   u = 6.24 m/s

   Correct Option: A

   u =	-1 δP	(R² - r²)
   	4μδx

   
   

   =	-1	× (-10)((0.05)² - (0.002)²)
   	4μδx

   
   u = 6.24 m/s

---

65. Air (ρ = 1.2 kg/m³ and kinematic viscosity, υ = 2 × 10^-5 m²/s) with a velocity of 2 m/s flows over the top surface of a flat plate of length 2.5 m. If the average value of friction coefficient is
    

    Cf =	1.328
    	√Rex

    
    the total drag force (in N) per unit width of the plate is _________.

1. 1. 0.1159

   
   
   

   2. 0.0259

   
   
   

   3. 0.0157

   
   
   

   4. 0.0159

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Cf =	1.320
   	√Rex

   
   

   Rex =	ρvd	=	vd.
   	μ		υ

   
   v = 2m/s
   1 = 2.5m
   υ = 2 × 10^–5 m²/s
   F = 1/2 C^fρAυ²
   A = 2.5 × 1
   On substituting we get
   F = 0.0159N

   Correct Option: D

   Cf =	1.320
   	√Rex

   
   

   Rex =	ρvd	=	vd.
   	μ		υ

   
   v = 2m/s
   1 = 2.5m
   υ = 2 × 10^–5 m²/s
   F = 1/2 C^fρAυ²
   A = 2.5 × 1
   On substituting we get
   F = 0.0159N

---