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The Bernoulli equation for steady frictionless incompressible flow along a streamline between two locations 1 and...
In-class Activity #4b Name Fluid Mechanics I (4600:310:301, Summer 2030,6/25, Thursday) Application of the Bernoulli Equation...
In-class Activity #4b Name Fluid Mechanics I (4600:310:301, Summer 2030,6/25, Thursday) Application of the Bernoulli Equation along a Streamline 1. Bernoulli equation along a streamline: Assumptions involved in Bernoulli equation: 1 No viscous effects (no shear) 2. Steady flow 3. Incompressible (density is constant) 4. Along a streamline P+ + Pgz=constant along streamline 2. The Static Pressure (p), Dynamic pressure, Stagnation pressure, and Total Pressure: Dynamic pressure: 1 Pd= 20v? Stagnation pressure: Ps= ptzov? Total pressure: P/ + Example 3.8...
Which one of the following is not an assumption of Bernoulli equation? -The flow is steady...
Which one of the following is not an assumption of Bernoulli equation? -The flow is steady -No elevation change -The flow is incompressible -There is no friction -There is no shaft work
Air flow over a cylinder of radius R- 150mm is modelled as a steady, frictionless and incompressible flow. The vector form of the velocity field is 1" The freestream velocity far away from the cy...
Air flow over a cylinder of radius R- 150mm is modelled as a steady, frictionless and incompressible flow. The vector form of the velocity field is 1" The freestream velocity far away from the cylinder is 75m/s and the static pressure is 101.3kPa. Note that this is similar to worked example 5.1 done during the lecture. However, now you know the Bernoulli equation can be used along a streamline...so: Find a) The stagnation pressure at the leading edge of the...
Bernoulli equation. The Bernoulli equation is a special case of conservation of linear momentum law of...
Bernoulli equation. The Bernoulli equation is a special case of conservation of linear momentum law of conservation of energy) for steady frictionless flow. This equation can be arrived at in three different ways. The usual form of the Bernoulli equation is: 1. pv2 + P + ?9z-constant a) For frictionless flow at steady state, Euler's equation of conservation of linear momentum reduces to: Starting from this equation, derive the Bernoulli equation. Assume irrotational flow. Derive the Bernoulli equation using the...
L 2. Steady statemass balance: Water is flowing at steady state in a 0.1 meter-diameter pipe...
L 2. Steady statemass balance: Water is flowing at steady state in a 0.1 meter-diameter pipe with a maximum velocity (turbulent profile) of 0.3 meters/sec. The pipe then goes through an expansion, to where it is then flowing in a 0.5 meter-diameter pipe, and the flow regime has changed from turbulent to laminar. In the second section of pipe, calculate the velocity as (a) block flow profile (Vavg), and (b) maximum velocity in laminar flow profile? HINT: you will need...
For an ideal, incompressible fluid of density p, subject to a gravitational field g= -Vº' (here...
For an ideal, incompressible fluid of density p, subject to a gravitational field g= -Vº' (here Ø' is the gravitational potential) the Euler equation is: Div=-- Vp+g, Div = .v + (v.7)v Use vector identity v * (I xv) = -(v.7)v + rv2) to derive Bernoulli's equation: --v2--p - d' = const, along any streamline (dye path) in steady flow. (a) Use y (b) This question concerns free surface flow and hydraulic jumps. Incompressible inviscid fluid (water) is in steady,...
Water can be considered as a non-viscous incompressible fluid of density p. A laboratory set-up is...
Water can be considered as a non-viscous incompressible fluid of density p. A laboratory set-up is such that water flows through a pipe, exhibiting a laminar and steady-state flow. At the top end of the pipe, the flow tube has a cross-sectional area A and point 1 (located on the central streamline) is exposed to the ambient environment. The pipe drops through a A vertical distance h7 while its area decreases to when it reaches point 2 (also on the...
1 (a) A steady stream of water jet discharges from the nozzle with a uniform velocity...
1 (a) A steady stream of water jet discharges from the nozzle with a uniform velocity of 10 m/s at angle 60° as shown in Figure 1. The jet strikes a horizontal plate 2 m above the nozzle exit. Upon impact, part of the flow is guided towards the left while the remainder towards the right, and the plate is suspended in the air. The weight of the plate is 25 N. Assume frictionless flow along the plate and weight...
An incompressible fluid flows between two porous, parallel flat plates as shown in the Figure below....
An incompressible fluid flows between two porous, parallel flat plates as shown in the Figure below. An identical fluid is injected at a constant speed V through the bottom plate and simultaneously extracted from the upper plate at the same velocity. There is no gravity force in x and y directions (g-g,-0). Assume the flow to be steady, fully-developed, 2D, and the pressure gradient in the x direction to be a constant P = constant). (a) Write the continuity equation...
1. Atall cylindrical tank, held above ground on stilts, is partially filled with water. (See top...
1. Atall cylindrical tank, held above ground on stilts, is partially filled with water. (See top figure). The tank has a diameter, D. At time equal to zero, a hole of diameter d is poked in the bottom of the tank, where d<< D. Let z-0 correspond to the bottom of the tank. The initial fluid height is za. Had Use Bernoulli equation to assess the velocity of the fluid as it leaves the bottom of the tank as a...
In-class Activity #4b Name Fluid Mechanics I (4600:310:301, Summer 2030,6/25, Thursday) Application of the Bernoulli Equation along a Streamline 1. Bernoulli equation along a streamline: Assumptions involved in Bernoulli equation: 1 No viscous effects (no shear) 2. Steady flow 3. Incompressible (density is constant) 4. Along a streamline P+ + Pgz=constant along streamline 2. The Static Pressure (p), Dynamic pressure, Stagnation pressure, and Total Pressure: Dynamic pressure: 1 Pd= 20v? Stagnation pressure: Ps= ptzov? Total pressure: P/ + Example 3.8...
Air flow over a cylinder of radius R- 150mm is modelled as a steady, frictionless and incompressible flow. The vector form of the velocity field is 1" The freestream velocity far away from the cylinder is 75m/s and the static pressure is 101.3kPa. Note that this is similar to worked example 5.1 done during the lecture. However, now you know the Bernoulli equation can be used along a streamline...so: Find a) The stagnation pressure at the leading edge of the...
Bernoulli equation. The Bernoulli equation is a special case of conservation of linear momentum law of conservation of energy) for steady frictionless flow. This equation can be arrived at in three different ways. The usual form of the Bernoulli equation is: 1. pv2 + P + ?9z-constant a) For frictionless flow at steady state, Euler's equation of conservation of linear momentum reduces to: Starting from this equation, derive the Bernoulli equation. Assume irrotational flow. Derive the Bernoulli equation using the...
L 2. Steady statemass balance: Water is flowing at steady state in a 0.1 meter-diameter pipe with a maximum velocity (turbulent profile) of 0.3 meters/sec. The pipe then goes through an expansion, to where it is then flowing in a 0.5 meter-diameter pipe, and the flow regime has changed from turbulent to laminar. In the second section of pipe, calculate the velocity as (a) block flow profile (Vavg), and (b) maximum velocity in laminar flow profile? HINT: you will need...
For an ideal, incompressible fluid of density p, subject to a gravitational field g= -Vº' (here Ø' is the gravitational potential) the Euler equation is: Div=-- Vp+g, Div = .v + (v.7)v Use vector identity v * (I xv) = -(v.7)v + rv2) to derive Bernoulli's equation: --v2--p - d' = const, along any streamline (dye path) in steady flow. (a) Use y (b) This question concerns free surface flow and hydraulic jumps. Incompressible inviscid fluid (water) is in steady,...
Water can be considered as a non-viscous incompressible fluid of density p. A laboratory set-up is such that water flows through a pipe, exhibiting a laminar and steady-state flow. At the top end of the pipe, the flow tube has a cross-sectional area A and point 1 (located on the central streamline) is exposed to the ambient environment. The pipe drops through a A vertical distance h7 while its area decreases to when it reaches point 2 (also on the...
1 (a) A steady stream of water jet discharges from the nozzle with a uniform velocity of 10 m/s at angle 60° as shown in Figure 1. The jet strikes a horizontal plate 2 m above the nozzle exit. Upon impact, part of the flow is guided towards the left while the remainder towards the right, and the plate is suspended in the air. The weight of the plate is 25 N. Assume frictionless flow along the plate and weight...
An incompressible fluid flows between two porous, parallel flat plates as shown in the Figure below. An identical fluid is injected at a constant speed V through the bottom plate and simultaneously extracted from the upper plate at the same velocity. There is no gravity force in x and y directions (g-g,-0). Assume the flow to be steady, fully-developed, 2D, and the pressure gradient in the x direction to be a constant P = constant). (a) Write the continuity equation...
1. Atall cylindrical tank, held above ground on stilts, is partially filled with water. (See top figure). The tank has a diameter, D. At time equal to zero, a hole of diameter d is poked in the bottom of the tank, where d<< D. Let z-0 correspond to the bottom of the tank. The initial fluid height is za. Had Use Bernoulli equation to assess the velocity of the fluid as it leaves the bottom of the tank as a...
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