အရည်ဒိုင်းနမစ် - ပြဿနာများနှင့် ဖြေရှင်းချက်များ

အရည်ဒိုင်းနမစ် - ပြဿနာများနှင့် ဖြေရှင်းချက်များ

တော်ရီဆယ်လီရဲ့ သီအိုရမ်

1. A container filled with water and there is a hole, as shown in the figure below. If acceleration due to gravity is 10 ms^-2, what is the speed of water through that hole?

လူသိများသည် :

အမြင့် (အမြင့်) = ၈၅ စင်တီမီတာ – ၄၀ စင်တီမီတာ = ၄၅ စင်တီမီတာ = ၀.၄၅ မီတာ

ဆွဲငင်အားကြောင့် အရှိန် (ဂရမ်) = ၁၀ မီတာ/စက္ကန့်²

လိုချင်သည် : The speed of water (v)

ဖြေရှင်းချက်

Torricelli’s theorem states that the water leaves the hole with the same speed as an object free fall from the same height. Height (h) = 85 cm – 40 cm = 45 cm = 0.45 meters

Velocity of water is calculated using the equation of the လွတ်လပ်စွာ ကျဆင်းမှု :

v_t² = ၂ ဂါလံ

v_t² = ၂ gh = ၂(၁၀)(၅) = ၁၀၀

v_t = √၉၀၀ = ၃၀ မီတာ/စက္ကန့်

2. A container filled with water and there is a hole, as shown in figure below. If acceleration due to gravity is 10 ms^-2, what is the speed of water through that hole.

လူသိများသည် :

အမြင့် (အမြင့်) = ၁.၅ မီတာ – ၀.၂၅ မီတာ = ၁.၂၅ မီတာ

ဆွဲငင်အားကြောင့် အရှိန် (g) = 10 m/s²

လိုချင်သည် : The speed of water (v)

ဖြေရှင်းချက်

v_t² = ၂ gh = ၂(၁၀)(၅) = ၁၀၀

v_t = √၉၀၀ = ၃၀ မီတာ/စက္ကန့်

3. A container filled with water and there is a hole, as shown in figure below. If acceleration due to gravity is 10 ms^-2, what is the speed of water through that hole.

လူသိများသည် :

Height (h) = 1 m – 0.20 m = 0.8 meter

ဆွဲငင်အားကြောင့် အရှိန် (g) = 10 m/s²

လိုချင်သည် : The speed of water (v)

ဖြေရှင်းချက်

v_t² = ၂ gh = ၂(၁၀)(၅) = ၁၀၀

v_t = √၉၀၀ = ၃၀ မီတာ/စက္ကန့်

4. A container filled with water and there is a hole, as shown in figure below. If acceleration due to gravity is 10 ms^-2, what is the speed of water through that hole.

လူသိများသည် :

အမြင့် (အမြင့်) = ၂၀ စင်တီမီတာ = ၀.၂ မီတာ

ဆွဲငင်အားကြောင့် အရှိန် (g) = 10 m/s²

Wanted: The speed of water (v)

ဖြေရှင်းချက်

5. A container filled with water and there နှစ်ခုရှိပါတယ် အပေါက်s, အောက်ပါပုံတွင်ပြထားသည့်အတိုင်း။ What is the ratio of x₁ to x₂?

ဆိုလူတီon

Time interval of the water free fall from hole 1 :

h = 1/2 a t²

၅ = ၁/၂ (၁၀) တီ²

၈၀ = ၅ တန်²

t² = 0.8/5 = 0.16

t = ၆.၁၂ စက္ကန့်

Time interval of the water free fall from hole 2 :

h = 1/2 a t²

၅ = ၁/၂ (၁၀) တီ²

၈၀ = ၅ တန်²

t² = 0.5/5 = 0.1

t = √0.1 second

အလျားလိုက်အကွာအဝေး (x):

x₁ = v₁ t₁ = (၄.၉)(၄) = ၁၉.၆ မီတာ

x₂ = v₂ t₂ = (√10)(√0.1) = (10)(0.1) = 1 meter

The ration of x₁ to x₂ :

x_{1 :} x₂ = 0.8 : 1 = 8 : 10 = 4 : 5

စဉ်ဆက်မပြတ်ဖြစ်မှုညီမျှခြင်း

6. Water flows through a pipe of varying diameter, A to B and then to C. The ratio of A to C is 8 : 3. If the speed of water in pipe A is v, what is the speed of water in pipe C.

လူသိများသည် :

Area of A (A_A) = 8

Area of C (A_C) = 3

The speed of water in pipe A (v_A) = v

Wanted: The speed of water in pipe C (v_C)

ဖြေရှင်းချက်

စဉ်ဆက်မပြတ်ဖြစ်မှု ညီမျှခြင်း-

A_A v_A = တစ် ဦး_C v_C

၈ ဗို့ = ၃ ဗို့_C

v_C = ၁/၂ ဗီ

7. If the speed of water in pipe with a diameter of 12 cm is 10 cm/s, what is the speed of water in a pipe with a diameter of 8 cm?

လူသိများသည် :

အချင်း ၁ (ဃ)₁) = 12 cm, radius 1 (r₁) = ၃၀ စင်တီမီတာ

အချင်း ၁ (ဃ)₂) = 8 cm, radius 2 (r₂) = ၃၀ စင်တီမီတာ

The speed of water 1 (v₁) = ၁၀ စင်တီမီတာ/စက္ကန့်

လိုချင်သည် : The speed of water 2 (v₂)

ဖြေရှင်းချက်

Area 1 (A₁) = π r² = π ၆² = ၃၆π စင်တီမီတာ²

Area 2 (A₂) = π r² = π ၆² = ၃၆π စင်တီမီတာ²

စဉ်ဆက်မပြတ်ဖြစ်မှု ညီမျှခြင်း-

A₁ v₁ = တစ် ဦး₂ v₂

(၃၆π)(၁၀) = (၁၆π) v₂

(၃၆)(၁၀) = (၁၆) v₂

၃၆၀ = (၁၆) v₂

v₂ = 360 / 16

v₂ = ၂၂.၅ စင်တီမီတာ/စက္ကန့်

8. Water flows through a pipe of varying diameter, as shown in figure below. If area 1 (A₁) = ၃၀ စင်တီမီတာ², တစ်ဦးက₂ = ၉၊၄ စင်တီမီတာ² and the speed of water in pipe 2 = v₂ = 2 m/s then what is the speed of water in pipe 1 = v₁.

လူသိများသည် :

Area 1 (A₁) = ၃၀ စင်တီမီတာ²

Area 2 (A₂) = ၃၀ စင်တီမီတာ²

Speed of water in pipe 2 (v₂) = ၂ မီတာ/စက္ကန့်

လိုချင်သည် : the speed of water in pipe 1 (v₁)

ဖြေရှင်းချက်

စဉ်ဆက်မပြတ်ဖြစ်မှု ညီမျှခြင်း-

A₁ v₁ = တစ် ဦး₂ v₂

8 v₁ = (၀.၁)(၀.၂)

8 v₁ = 4

v₁ = ၄ / ၈ = ၀.၅ မီတာ/စက္ကန့်

9. If the diameter of the larger pipe is 2 times the diameter of smaller pipe, what is the speed of fluid at the smaller pipe.

လူသိများသည် :

Diameter of the larger pipe (d₁) = 2

Radius of the larger pipe (r₁) = ½ ရက်₁ = ½ (၄) = ၂

Area of the larger pipe (A₁) = π r₁² = π (1)² = π (1) = π

Diameter of the smaller pipe (d₂) = 1

Radius of the smaller pipe (r₂) = ½ ရက်₂ = ½ (၁) = ½

Area of the smaller pipe (A₂) = π r₂² = π (၁/၂)² = π (၁/၄) = ¼ π

The speed of fluid at the larger pipe (v₁) = ၂ မီတာ/စက္ကန့်

လိုချင်သည် : The speed of fluid at the smaller pipe (v₂)

ဖြေရှင်းချက်

စဉ်ဆက်မပြတ်ဖြစ်မှု ညီမျှခြင်း-

A₁ v₁ = တစ် ဦး₂ v₂

π ၄ = ¼ π (v)₂)

၄ = ¼ (v)₂)

v₂ = ၉.၈ မီတာ/စက္ကန့်

Bernoulli’s principle and equation

10 ။ W ကater is pumped with a 120 kPa compressor entering the lower pipe (1) and flows upward at a speed of 1 m/s. Acceleration due to gravity is ၂၀ မီတာ/s and water density is 1000 ကီလိုဂရမ် / မီတာ^-3. t ကိုကဘာလဲhe water pressure on the upper pipe (II).

လူသိများသည် :

Radius of the lower pipe (r₁) = ၃၀ စင်တီမီတာ

Radius of the lower pipe (r₂) = ၃၀ စင်တီမီတာ

Water pressure in the lower pipe (p₁) = ၁၂၀ kPa = ၁၂၀,၀၀၀ ပါစကယ်

The speed of water in the lower pipe (v₁) = 1 မီလီစက္ကန့်^-1

The height of the lower pipe (h₁) = ၀ မီတာ

The height of the upper pipe (h₂) = ၀ မီတာ

ဆွဲငင်အားကြောင့် အရှိန်မြှင့်ခြင်း (g) = 10 ms^-2

Density of water = 1000 kg.m^-3

Wanted: Water pressure in pipe 2 (p₂)

ဖြေရှင်းချက်

The speed of water in pipe 2 is calculated with the equation of continuity :

Water pressure in pipe 2 is calculated using the equation of Bernoulli :

11. A large pipe 5 meters above the ground and a small pipe 1 meter above the ground. The velocity of the water in a large pipe is 36 km / h with a pressure of 9.1 x 10⁵ Pa, while the pressure in the small pipe is 2.10⁵ pa ။ ဘာဖြစ်သလဲ the water velocity in the small pipe? ရေ density = 10³ ကီလိုဂရမ် / မီတာ³

လူသိများသည် :

Water pressure in the large pipe (p₁) = ၂၂ x ၁၀⁵ ပါစကယ် = ၉၁၀,၀၀၀ ပါစကယ်

Water pressure in the small pipe (p₂) = ၂၂ x ၁၀⁵ ပါစကယ် = ၉၁၀,၀၀၀ ပါစကယ်

Water speed in the large pipe (v₁) = 36 km/h = 36(1000)/(3600) = 36000/3600 =10 m/s

The height of the large pipe (h₁) = -4 meters

The height of the small pipe (h₂) = ၅ မီတာ

ဆွဲငင်အားကြောင့် အရှိန်မြှင့်ခြင်း (g) = 10 ms^-2

Density of water = 1000 kg/m³

Wanted: The speed of water in the small pipe (v₂)

ဖြေရှင်းချက်

The speed of water in the small pipe (v₂) is calculated using the equation of Bernoulli :

12. A pipe နှင့် အချင်းဝက်တစ်ခု of 15 cm connected with another pipe with a radius of 5 cm. Both are in a horizontal position. The velocity of the water flow in the large pipe is 1 m/s at a pressure of 10⁵ N/m². t ကိုကဘာလဲhe ရေ pressure on the small pipe (1 g cm^-3)

လူသိများသည် :

Radius of the large pipe (r₁) = ၄ စင်တီမီတာ = ၀.၀၄ မီတာ

Radius of the small pipe (r₂) = ၄ စင်တီမီတာ = ၀.၀၄ မီတာ

The water pressure in the large pipe (p₁) = 10⁵ n m^-2 = ၁၀၀,၀၀၀ N m^-2

The speed of water in the large pipe (v₁) = 1 မီလီစက္ကန့်^-1

ဆွဲငင်အားကြောင့် အရှိန်မြှင့်ခြင်း (g) = 10 ms^-2

ရေ သိပ်သည်းဆ = ၁.၅ ဂရမ် စင်တီမီတာ^-3 = ၀.၁၂၇ ကီလိုဂရမ် မီတာ^-3

Height difference (Δh) = 0.

Wanted: Pressure in the small pipe (p₂)

ဖြေရှင်းချက်

The speed of water in pipe 2 is calculated using the equation of continuity :

The water pressure in the small pipe (p₂) is calculated using the equation of Bernoulli :

1. What is fluid dynamics?
   • အဖြေ: Fluid dynamics is the branch of physics that studies the motion of fluids (liquids and gases) and the forces acting on them. It encompasses the principles and equations that describe how fluids flow, interact with solid boundaries, and affect one another.
2. What’s the difference between laminar and turbulent flow?
   • အဖြေ: Laminar flow is characterized by smooth, parallel layers of fluid moving in orderly paths. Turbulent flow, on the other hand, is chaotic, with eddies, swirls, and rapid fluctuations. Turbulence generally occurs at high velocities or in irregularly shaped channels.
3. How is the concept of viscosity important in fluid dynamics?
   • အဖြေ: Viscosity measures a fluid’s resistance to shear or flow. High-viscosity fluids (like honey) resist flow more than low-viscosity fluids (like water). In fluid dynamics, viscosity plays a crucial role in determining the nature of fluid flow, energy dissipation, and drag forces.
4. What is Bernoulli’s principle?
   • အဖြေ: Bernoulli’s principle states that in a steady flow, the sum of pressure energy, kinetic energy, and potential energy per unit volume remains constant. Specifically, where the fluid velocity is high, the pressure is low, and vice versa.
5. How does the principle of lift in aerodynamics relate to fluid dynamics?
   • အဖြေ: The lift on an aircraft wing can be explained using Bernoulli’s principle and Newton’s third law. As air flows over the wing, it moves faster over the curved top surface than the bottom, creating a pressure difference. This difference in pressure, combined with the downward deflection of air by the wing, results in an upward force or lift.
6. What is the equation of continuity in fluid dynamics?
   • အဖြေ: The equation of continuity states that the product of the cross-sectional area (A) of a flow and its velocity (v) remains constant along a streamline in a steady flow. Mathematically, A₁​v_1​=A₂​v₂​အဘယ်မှာရှိသနည်း A_1​ နှင့် A₂​ are cross-sectional areas and v₁​ နှင့် v_2​ are the velocities at two points along the streamline.
7. What role does the Reynolds number play in fluid dynamics?
   • အဖြေ: The Reynolds number is a dimensionless quantity that helps predict the flow regime (laminar, transitional, or turbulent) in fluid dynamics. It’s defined as the ratio of inertial forces to viscous forces and depends on factors like fluid velocity, characteristic length, and fluid properties.
8. How does the drag force act on objects moving in a fluid?
   • အဖြေ: Drag force opposes the motion of an object through a fluid. It arises due to the viscous resistance of the fluid and the pressure differences around the object. The magnitude and nature of drag depend on factors like the object’s shape, roughness, speed, and the properties of the fluid.
9. What is the Venturi effect?
   • အဖြေ: The Venturi effect refers to the decrease in fluid pressure that occurs when a fluid flows through a constricted section of a pipe. As the fluid’s velocity increases in the constricted section (due to the conservation of mass), its pressure decreases according to Bernoulli’s principle.
10. Why does fluid speed up when flowing through a narrow section of a pipe or channel?

• အဖြေ: This behavior can be explained by the principle of conservation of mass. In a steady flow, the volume of fluid entering a section of a pipe must equal the volume leaving. If the pipe narrows, the fluid must speed up to allow the same volume to pass through in a given time.