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A fire hose nozzle directs a steady stream of water of velocity 50 m/s at an angle of 45° above the horizontal. The stream rises initially but then eventually falls to the ground. Assume water as incompressible and inviscid. Consider the density of air and the air friction as negligible and assume the acceleration due to gravity as 9.81 m/s2. The maximum height (in m, round off to two decimal places) reached by the stream above the hose nozzle will then be __________.
Correct answer is '63.71'. Can you explain this answer?
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A fire hose nozzle directs a steady stream of water of velocity 50 m/...
Equation of motion in y-direction:
Vf ➡ Final velocity
Vi ➡ Initial velocity
At S = H, Vfy = 0, a = -g
Viy = Vo sin45°
Substituting values in equation (1),
0 = (V sin 45)2 + 2(-g) H
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A fire hose nozzle directs a steady stream of water of velocity 50 m/...
Understanding the Problem:
We have a fire hose nozzle that directs a steady stream of water at an angle of 45° above the horizontal. We need to determine the maximum height reached by the stream above the nozzle.
Given Data:
- Water velocity: 50 m/s
- Angle of the stream above the horizontal: 45°
- Acceleration due to gravity: 9.81 m/s²
Assumptions:
- Negligible density of air and air friction.
- Water is incompressible and inviscid.
Analysis:
To solve this problem, we can break down the motion of the water stream into horizontal and vertical components. Let's consider the vertical component first.
Vertical Motion:
The initial vertical velocity of the water stream is given by the equation:
v₀y = v₀ * sin(θ)
where v₀ is the initial velocity of the water stream and θ is the angle of the stream above the horizontal.
In this case, v₀ = 50 m/s and θ = 45°. Plugging in these values, we can find the initial vertical velocity:
v₀y = 50 * sin(45°)
v₀y = 50 * √2 / 2
v₀y = 50√2 / 2
v₀y = 25√2 m/s
The maximum height reached by the water stream can be calculated using the equation for vertical motion:
Δy = v₀y² / (2g)
where Δy is the maximum height reached, v₀y is the initial vertical velocity, and g is the acceleration due to gravity.
Plugging in the values, we get:
Δy = (25√2)² / (2 * 9.81)
Δy = 625 * 2 / 19.62
Δy ≈ 63.71 m
Answer:
Therefore, the maximum height reached by the water stream above the hose nozzle is approximately 63.71 meters.
We have a fire hose nozzle that directs a steady stream of water at an angle of 45° above the horizontal. We need to determine the maximum height reached by the stream above the nozzle.
Given Data:
- Water velocity: 50 m/s
- Angle of the stream above the horizontal: 45°
- Acceleration due to gravity: 9.81 m/s²
Assumptions:
- Negligible density of air and air friction.
- Water is incompressible and inviscid.
Analysis:
To solve this problem, we can break down the motion of the water stream into horizontal and vertical components. Let's consider the vertical component first.
Vertical Motion:
The initial vertical velocity of the water stream is given by the equation:
v₀y = v₀ * sin(θ)
where v₀ is the initial velocity of the water stream and θ is the angle of the stream above the horizontal.
In this case, v₀ = 50 m/s and θ = 45°. Plugging in these values, we can find the initial vertical velocity:
v₀y = 50 * sin(45°)
v₀y = 50 * √2 / 2
v₀y = 50√2 / 2
v₀y = 25√2 m/s
The maximum height reached by the water stream can be calculated using the equation for vertical motion:
Δy = v₀y² / (2g)
where Δy is the maximum height reached, v₀y is the initial vertical velocity, and g is the acceleration due to gravity.
Plugging in the values, we get:
Δy = (25√2)² / (2 * 9.81)
Δy = 625 * 2 / 19.62
Δy ≈ 63.71 m
Answer:
Therefore, the maximum height reached by the water stream above the hose nozzle is approximately 63.71 meters.
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A fire hose nozzle directs a steady stream of water of velocity 50 m/s at an angle of 45° above the horizontal. The stream rises initially but then eventually falls to the ground. Assume water as incompressible and inviscid. Consider the density of air and the air friction as negligible and assume the acceleration due to gravity as 9.81 m/s2. The maximum height (in m, round off to two decimal places) reached by the stream above the hose nozzle will then be __________.Correct answer is '63.71'. Can you explain this answer?
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A fire hose nozzle directs a steady stream of water of velocity 50 m/s at an angle of 45° above the horizontal. The stream rises initially but then eventually falls to the ground. Assume water as incompressible and inviscid. Consider the density of air and the air friction as negligible and assume the acceleration due to gravity as 9.81 m/s2. The maximum height (in m, round off to two decimal places) reached by the stream above the hose nozzle will then be __________.Correct answer is '63.71'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A fire hose nozzle directs a steady stream of water of velocity 50 m/s at an angle of 45° above the horizontal. The stream rises initially but then eventually falls to the ground. Assume water as incompressible and inviscid. Consider the density of air and the air friction as negligible and assume the acceleration due to gravity as 9.81 m/s2. The maximum height (in m, round off to two decimal places) reached by the stream above the hose nozzle will then be __________.Correct answer is '63.71'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A fire hose nozzle directs a steady stream of water of velocity 50 m/s at an angle of 45° above the horizontal. The stream rises initially but then eventually falls to the ground. Assume water as incompressible and inviscid. Consider the density of air and the air friction as negligible and assume the acceleration due to gravity as 9.81 m/s2. The maximum height (in m, round off to two decimal places) reached by the stream above the hose nozzle will then be __________.Correct answer is '63.71'. Can you explain this answer?.
A fire hose nozzle directs a steady stream of water of velocity 50 m/s at an angle of 45° above the horizontal. The stream rises initially but then eventually falls to the ground. Assume water as incompressible and inviscid. Consider the density of air and the air friction as negligible and assume the acceleration due to gravity as 9.81 m/s2. The maximum height (in m, round off to two decimal places) reached by the stream above the hose nozzle will then be __________.Correct answer is '63.71'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A fire hose nozzle directs a steady stream of water of velocity 50 m/s at an angle of 45° above the horizontal. The stream rises initially but then eventually falls to the ground. Assume water as incompressible and inviscid. Consider the density of air and the air friction as negligible and assume the acceleration due to gravity as 9.81 m/s2. The maximum height (in m, round off to two decimal places) reached by the stream above the hose nozzle will then be __________.Correct answer is '63.71'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A fire hose nozzle directs a steady stream of water of velocity 50 m/s at an angle of 45° above the horizontal. The stream rises initially but then eventually falls to the ground. Assume water as incompressible and inviscid. Consider the density of air and the air friction as negligible and assume the acceleration due to gravity as 9.81 m/s2. The maximum height (in m, round off to two decimal places) reached by the stream above the hose nozzle will then be __________.Correct answer is '63.71'. Can you explain this answer?.
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