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Problem Chapter 1

The document contains a series of physics problems related to fluid mechanics, including calculations for bulk modulus of elasticity, gas pressure, viscous shear force, shear stress, and dynamic viscosity. Each problem is followed by its corresponding answer, providing insights into the behavior of liquids and gases under various conditions. Key parameters such as pressure, volume, velocity, and viscosity are utilized to derive the solutions.

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5 views3 pages

Problem Chapter 1

The document contains a series of physics problems related to fluid mechanics, including calculations for bulk modulus of elasticity, gas pressure, viscous shear force, shear stress, and dynamic viscosity. Each problem is followed by its corresponding answer, providing insights into the behavior of liquids and gases under various conditions. Key parameters such as pressure, volume, velocity, and viscosity are utilized to derive the solutions.

Uploaded by

hieu.trantienminh06
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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CHAPTER 1

Problem 1.8 A liquid completely fills a cylinder with volume V = 25 cm³. When the piston
is compressed and the pressure increases by 15 at, the volume of the liquid in the cylinder
decreases to 24.9 cm³. Determine the bulk modulus of elasticity of the liquid.
Answer: 3.68 × 10⁸ N/m²

Problem 1.9 A gas container has volume V₀ = 1 m³ with absolute pressure p₀ = 1 at.
Additional gas is injected through a side valve until the container reaches an absolute
pressure of p₁ = 3 at. The volume of gas added is 60 m³. Determine the absolute pressure
of the gas before being injected. Assume isothermal compression and a rigid container.

Answer: 0.033 at

Problem 1.13 A flat plate of area A = ab moves


y V
with velocity V = 4.5 m/s on a horizontal surface
covered by an oil layer of thickness h = 20 mm. The u
h
oil has specific gravity = 0.8 and kinematic viscosity
ν = 5×10⁻⁴ m²/s. The velocity measured at position y
Fig. 1.13
= h/2 is 2.0 m/s. The velocity distribution in the oil
layer is given as u = C₁y² + C₂y. Given a = 1.0 m and b = 0.5 m, determine the viscous
shear force acting on the bottom of the plate.

Answer: 55 N

Problem 1.14 Wind blows over the water surface with velocity distribution u = 1085y –
108y³ (m/s), where y is in meters. The kinematic viscosity of air is ν = 15.1×10⁻⁶ m²/s and
the density of air is 1.2 kg/m³. Calculate the shear stress on the water surface.

Answer: 0.0197 N/m²


Problem 1.16 Oil flows in a narrow gap of thickness 2t
= 10 mm with velocity V = 0.02 m/s. In the middle of t A
V
the gap, there is a flat plate of area A = 0.2 m². The oil t

has dynamic viscosity μ = 8.14×10⁻² Pa·s. Determine the Fig. 1.16


force F required to pull the plate A so that it does not
drift with the flow.

Answer: 0.13 N
Vo
Problem 1.17 Two liquid layers of equal thickness t have
dynamic viscosities μ₁ = 0.4 N·s/m² and μ₂ = 0.2 N·s/m². On
1 t
the free surface of the first liquid layer, a flat plate moves
with velocity V₀ = 3 m/s. The bottom of the second liquid
V
layer is fixed. Assume linear velocity distribution in both 2 t

layers. Determine the velocity V at the interface between


the two layers. Fig. 1.17

Answer: 2 m/s

Problem 1.19 The dynamic viscosity μ of an oil can be determined experimentally as


shown in the figure. Given: V = 0.5 m/s; t = 1.25 mm; square plate side a = 1 m; plate
weight G = 200 N; inclination angle θ = 20°. Neglect the weight of the oil layer. Determine
μ.

Answer: 0.171 Pa·s

a t

V
G

Fig. 1.19
Problem 1.22 A circular shaft of diameter D=4cm rotates in a bearing of length L=5 cm.
The narrow clearance between the shaft and the bearing is t=0.02 mm, lubricated with oil
of viscosity μ=0.03 Pa.s. The shaft rotates at 150 rpm. Determine the power loss due to
viscous friction.

Answer: 0.929 W

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