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Questions and Answers
The momentum equation is used to determine the resultant force acting on the boundary of _____ passage by a stream of fluid.
The momentum equation is used to determine the resultant force acting on the boundary of _____ passage by a stream of fluid.
flow
The continuity of mass flow across the control volume can be expressed as 𝜌1 𝐴1 ______ = 𝜌2 𝐴2 𝑣2 = ṁ
The continuity of mass flow across the control volume can be expressed as 𝜌1 𝐴1 ______ = 𝜌2 𝐴2 𝑣2 = ṁ
𝑣1
The rate of change of momentum of fluid in x-direction is given by 𝐹𝑥 = 𝑚̇(𝑣2 ____ 𝑣1 𝑐𝑜𝑠𝜃).
The rate of change of momentum of fluid in x-direction is given by 𝐹𝑥 = 𝑚̇(𝑣2 ____ 𝑣1 𝑐𝑜𝑠𝜃).
cos∅
The rate of change of ______ across the control volume can be expressed as 𝜌2 𝐴2 𝑣2 𝑣2 − 𝜌1 𝐴1 𝑣1 𝑣1
The rate of change of ______ across the control volume can be expressed as 𝜌2 𝐴2 𝑣2 𝑣2 − 𝜌1 𝐴1 𝑣1 𝑣1
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The ______ equation for 1-dimensional flow in a straight line is 𝐹 = 𝑚(𝑣2 − 𝑣1 )
The ______ equation for 1-dimensional flow in a straight line is 𝐹 = 𝑚(𝑣2 − 𝑣1 )
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The total force exerted on the fluid in a control volume in a given direction is equal to the rate of change of _____ in the given direction of fluid passing through the control volume.
The total force exerted on the fluid in a control volume in a given direction is equal to the rate of change of _____ in the given direction of fluid passing through the control volume.
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The force F is the resultant force acting on the fluid element ABCD in the direction of ______
The force F is the resultant force acting on the fluid element ABCD in the direction of ______
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The force exerted by the fluid on the surroundings will be equal and _____ to the resultant force.
The force exerted by the fluid on the surroundings will be equal and _____ to the resultant force.
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The momentum equation is used to calculate the ______ exerted by the fluid on its surroundings
The momentum equation is used to calculate the ______ exerted by the fluid on its surroundings
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The momentum equation is used to solve problems involving _____ enlargement in a pipe.
The momentum equation is used to solve problems involving _____ enlargement in a pipe.
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The component velocities in the z-direction are denoted by 𝑉𝑧1 and 𝑉𝑧2 in the case of _____ flow.
The component velocities in the z-direction are denoted by 𝑉𝑧1 and 𝑉𝑧2 in the case of _____ flow.
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In a 2-dimensional problem, the velocity 𝑣1 makes an angle of 𝜃 with the ______-axis
In a 2-dimensional problem, the velocity 𝑣1 makes an angle of 𝜃 with the ______-axis
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The momentum and force are resolved into components in the ______ and y directions
The momentum and force are resolved into components in the ______ and y directions
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The momentum equation is used to determine the characteristics of flow when there is an _____ change of flow section.
The momentum equation is used to determine the characteristics of flow when there is an _____ change of flow section.
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The mass flow rate per unit time is represented by the symbol ______
The mass flow rate per unit time is represented by the symbol ______
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The application of impulse-momentum equation is used to solve problems involving _____ propulsion.
The application of impulse-momentum equation is used to solve problems involving _____ propulsion.
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The velocity of a fluid in general is a function of _______ and time.
The velocity of a fluid in general is a function of _______ and time.
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The acceleration of a fluid is given by the equation 𝑎 = 𝑎𝑥 𝑖 + 𝑎𝑦 𝑗 + 𝑎𝑧 _______.
The acceleration of a fluid is given by the equation 𝑎 = 𝑎𝑥 𝑖 + 𝑎𝑦 𝑗 + 𝑎𝑧 _______.
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The resultant velocity of a fluid is given by the equation 𝑣 = √𝑢2 + 𝑣2 + 𝑤2, where 𝑣 is the _______ velocity.
The resultant velocity of a fluid is given by the equation 𝑣 = √𝑢2 + 𝑣2 + 𝑤2, where 𝑣 is the _______ velocity.
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The acceleration vector of a fluid is given by the equation 𝑎 = (𝑢 ∂x + 𝑣 ∂y + 𝑤 ∂z) + ∂_______.
The acceleration vector of a fluid is given by the equation 𝑎 = (𝑢 ∂x + 𝑣 ∂y + 𝑤 ∂z) + ∂_______.
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Fluid flow can be classified into _______ and unsteady flows.
Fluid flow can be classified into _______ and unsteady flows.
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The velocity vector of a fluid is given by the equation 𝑣 = 𝑢𝑖 + 𝑣𝑗 + 𝑤_______.
The velocity vector of a fluid is given by the equation 𝑣 = 𝑢𝑖 + 𝑣𝑗 + 𝑤_______.
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The magnitude of the acceleration vector of a fluid is given by the equation |𝑎| = √𝑎𝑥2 + 𝑎𝑦2 + 𝑎𝑧2, where 𝑎 is the _______ acceleration.
The magnitude of the acceleration vector of a fluid is given by the equation |𝑎| = √𝑎𝑥2 + 𝑎𝑦2 + 𝑎𝑧2, where 𝑎 is the _______ acceleration.
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Vectorially, the acceleration of a fluid is given by the equation 𝑎 = (𝑉.∇)𝑉 + ∂_______.
Vectorially, the acceleration of a fluid is given by the equation 𝑎 = (𝑉.∇)𝑉 + ∂_______.
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Study Notes
Momentum Equation for Two-Dimensional Flow
- The momentum equation is used to solve problems involving a stream of fluid changing its direction, magnitude, or both.
- The equation is also used to determine the characteristics of flow when there is an abrupt change of flow section.
Components of Force
- 𝐹𝑥 = 𝑚̇(𝑣2 𝑐𝑜𝑠∅ − 𝑣1 𝑐𝑜𝑠𝜃) = 𝑚̇(𝑣𝑥2 − 𝑣𝑥1), the rate of change of momentum of fluid in x-direction.
- 𝐹𝑦 = 𝑚̇(𝑣2 𝑠𝑖𝑛∅ − 𝑣1 𝑠𝑖𝑛𝜃) = 𝑚̇(𝑣𝑦2 − 𝑣𝑦1), the rate of change of momentum of fluid in y-direction.
- The resultant force is given by 𝐹 = √(𝐹𝑥 2 + 𝐹𝑦 2).
Momentum Equation for Three-Dimensional Flow
- For three-dimensional flow, the fluid will also have component velocities 𝑉𝑧1 and 𝑉𝑧2 in the z-direction.
- The corresponding rate of change of momentum in this direction will require the force 𝐹𝑧 = 𝑚̇(𝑣𝑧2 − 𝑣𝑧1).
Application of Impulse-Momentum Equation
- The momentum equation is used to solve problems involving:
- Pipe bends, reducers, moving vanes, and jet propulsion.
- Sudden enlargement in a pipe and hydraulic jump in a channel.
Example Problem
- Water flows in a pipe of diameter 300 mm at 250 liters/sec, with a pressure of 400 KN/m2.
- If the pipe is bent by 135⁰C, find the magnitude and direction of the resultant force on the bend.
Continuity of Mass Flow
- The continuity of mass flow across the control volume can be expressed as 𝜌1 𝐴1 𝑣1 = 𝜌2 𝐴2 𝑣2 = 𝑚̇.
- The rate of change of momentum across the control volume can be expressed as 𝜌2 𝐴2 𝑣2 𝑣2 − 𝜌1 𝐴1 𝑣1 𝑣1.
Momentum Equation for 1-Dimensional Flow
- The momentum equation for 1-dimensional flow in a straight line is given by 𝐹 = 𝑚(𝑣2 − 𝑣1), which is equivalent to Newton's second law of motion.
Momentum Equation for Two- and Three-Dimensional Flow
- The momentum equation for two- and three-dimensional flow along a streamline can be expressed in vector notation as 𝑎 = 𝑎𝑥 𝑖 + 𝑎𝑦 𝑗 + 𝑎𝑧 𝑘.
- The acceleration vector can be written as 𝑎 = (𝑢 ∂x + 𝑣 ∂y + 𝑤 ∂z) + ∂t.
Types of Fluid Flow
- Fluid flow can be classified as:
- Steady flow and unsteady flows
- Uniform and non-uniform flows
- One, two-, and three-dimensional flows
- Rotational and irrotational flows
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Description
Learn about the momentum equation for two-dimensional flow, including the components of the resultant force and their relation to mass and velocity.
