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A pipe line 0.2m in diameter flowing full of water has a construction of diameter 0.1m.if the velocity in the 0.2m pipe line in 2m/s calculate 1.the velocity in the construction? and 2.the discharge rate in cubic metre per second?
Verified Answer
A pipe line 0.2m in diameter flowing full of water has a construction ...
To calculate the velocity in the construction and the discharge rate in cubic metres per second, we can use the following formulas:
Velocity in the construction:
Vc = (Vp * Dp) / Dc
Where Vc is the velocity in the construction, Vp is the velocity in the pipe, Dp is the diameter of the pipe, and Dc is the diameter of the construction.
Discharge rate in cubic metres per second:
Q = (π/4) * Dp^2 * Vp
Where Q is the discharge rate in cubic metres per second, π is the constant approximately equal to 3.14, Dp is the diameter of the pipe, and Vp is the velocity in the pipe.
Plugging in the given values, we get:
Velocity in the construction:
Vc = (2 * 0.2) / 0.1 = 4 m/s
Discharge rate in cubic metres per second:
Q = (π/4) * 0.2^2 * 2 = 0.0314 m^3/s
Therefore, the velocity in the construction is 4 m/s and the discharge rate in cubic metres per second is 0.0314 m^3/s.
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Most Upvoted Answer
A pipe line 0.2m in diameter flowing full of water has a construction ...
1. Velocity in the construction:
To calculate the velocity in the construction, we can use the principle of continuity, which states that the mass flow rate of a fluid remains constant within a closed system.
The formula for the principle of continuity is:
A1 * V1 = A2 * V2
Where:
A1 and A2 are the cross-sectional areas of the pipe and construction respectively, and
V1 and V2 are the velocities in the pipe and construction respectively.
Given that the diameter of the pipe is 0.2m and the diameter of the construction is 0.1m, we can calculate the areas:
A1 = π * (0.2/2)^2 = 0.0314 m^2
A2 = π * (0.1/2)^2 = 0.00785 m^2
We are also given that the velocity in the pipe (V1) is 2 m/s. Let's substitute the values into the continuity equation:
0.0314 * 2 = 0.00785 * V2
Simplifying the equation, we find:
V2 = (0.0314 * 2) / 0.00785
V2 ≈ 7.96 m/s
Therefore, the velocity in the construction is approximately 7.96 m/s.
2. Discharge rate in cubic meters per second:
The discharge rate (Q) is the volume of fluid passing through a given cross-sectional area per unit time. It can be calculated using the formula:
Q = A * V
Where:
Q is the discharge rate,
A is the cross-sectional area, and
V is the velocity.
We already know the velocity in the construction (V2 ≈ 7.96 m/s) and the cross-sectional area of the construction (A2 ≈ 0.00785 m^2).
Substituting these values into the formula, we can find the discharge rate:
Q = 0.00785 * 7.96
Q ≈ 0.0624 m^3/s
Therefore, the discharge rate is approximately 0.0624 cubic meters per second.
To summarize:
1. The velocity in the construction is approximately 7.96 m/s.
2. The discharge rate is approximately 0.0624 cubic meters per second.
To calculate the velocity in the construction, we can use the principle of continuity, which states that the mass flow rate of a fluid remains constant within a closed system.
The formula for the principle of continuity is:
A1 * V1 = A2 * V2
Where:
A1 and A2 are the cross-sectional areas of the pipe and construction respectively, and
V1 and V2 are the velocities in the pipe and construction respectively.
Given that the diameter of the pipe is 0.2m and the diameter of the construction is 0.1m, we can calculate the areas:
A1 = π * (0.2/2)^2 = 0.0314 m^2
A2 = π * (0.1/2)^2 = 0.00785 m^2
We are also given that the velocity in the pipe (V1) is 2 m/s. Let's substitute the values into the continuity equation:
0.0314 * 2 = 0.00785 * V2
Simplifying the equation, we find:
V2 = (0.0314 * 2) / 0.00785
V2 ≈ 7.96 m/s
Therefore, the velocity in the construction is approximately 7.96 m/s.
2. Discharge rate in cubic meters per second:
The discharge rate (Q) is the volume of fluid passing through a given cross-sectional area per unit time. It can be calculated using the formula:
Q = A * V
Where:
Q is the discharge rate,
A is the cross-sectional area, and
V is the velocity.
We already know the velocity in the construction (V2 ≈ 7.96 m/s) and the cross-sectional area of the construction (A2 ≈ 0.00785 m^2).
Substituting these values into the formula, we can find the discharge rate:
Q = 0.00785 * 7.96
Q ≈ 0.0624 m^3/s
Therefore, the discharge rate is approximately 0.0624 cubic meters per second.
To summarize:
1. The velocity in the construction is approximately 7.96 m/s.
2. The discharge rate is approximately 0.0624 cubic meters per second.
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A pipe line 0.2m in diameter flowing full of water has a construction of diameter 0.1m.if the velocity in the 0.2m pipe line in 2m/s calculate 1.the velocity in the construction? and 2.the discharge rate in cubic metre per second?
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A pipe line 0.2m in diameter flowing full of water has a construction of diameter 0.1m.if the velocity in the 0.2m pipe line in 2m/s calculate 1.the velocity in the construction? and 2.the discharge rate in cubic metre per second? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A pipe line 0.2m in diameter flowing full of water has a construction of diameter 0.1m.if the velocity in the 0.2m pipe line in 2m/s calculate 1.the velocity in the construction? and 2.the discharge rate in cubic metre per second? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A pipe line 0.2m in diameter flowing full of water has a construction of diameter 0.1m.if the velocity in the 0.2m pipe line in 2m/s calculate 1.the velocity in the construction? and 2.the discharge rate in cubic metre per second?.
A pipe line 0.2m in diameter flowing full of water has a construction of diameter 0.1m.if the velocity in the 0.2m pipe line in 2m/s calculate 1.the velocity in the construction? and 2.the discharge rate in cubic metre per second? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A pipe line 0.2m in diameter flowing full of water has a construction of diameter 0.1m.if the velocity in the 0.2m pipe line in 2m/s calculate 1.the velocity in the construction? and 2.the discharge rate in cubic metre per second? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A pipe line 0.2m in diameter flowing full of water has a construction of diameter 0.1m.if the velocity in the 0.2m pipe line in 2m/s calculate 1.the velocity in the construction? and 2.the discharge rate in cubic metre per second?.
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