Fluid Mechanics Chapter 4 - Control Volume Analysis

The horizontal force required to hold a stationary plate in place when a jet of water strikes it, calculated by the change in momentum of the water.

The vertical force acting on a stationary plate due to water jet impacts; equal to zero, because flow rate remains unchanged.

The speed of the water jet striking the plate directly influences the force required to hold the plate in position.

The velocity at which the water strikes a moving plate relative to the plate's motion, calculated as the jet's velocity minus the plate's velocity.

Using Bernoulli's equation and momentum principles to calculate forces exerted by water jets on stationary or moving plates.

A body's momentum remains constant unless acted upon by an external force; the rate of change of momentum equals the applied force.

The product of mass and velocity of a body.

The momentum change per unit of time; equivalent to applied force.

A fixed region in space used to analyze fluid flow. Equations for flow, forces, and energy are applied to this region.

A fluid jet striking a flat plate; the reaction force is calculated using the change in momentum of the fluid.

Fluid flowing through a change in pipe size; the momentum change determines the force on the pipe.

The volume of fluid passing a point per unit of time. (e.g., cubic meters/second ).

Force equals the rate of change of momentum. Influid mechanics, the force on the fluid or body is due to the difference in momentum entering and leaving a control volume.

The turbulence created in the separation zone of a bend causes resistance to fluid flow. A larger bend radius reduces this resistance.

A fixed region in space used for examining fluid flow within a bend. It's like a box surrounding the bend, helping us analyze the forces acting on the fluid.

The horizontal force acting on the bend due to changes in fluid momentum and pressure. It's calculated as the difference between the pressure forces and the momentum change.

The vertical force acting on the bend due to pressure, weight, and momentum changes. It's calculated similarly to the x-direction force, but also includes the weight of the fluid.

The total force acting on the bend, calculated as the square root of the sum of the squared forces in the x and z directions. It's the combined effect of all forces.

A fundamental equation in fluid dynamics that relates the forces acting on a bend to the change in momentum of the fluid passing through it.

The angle of the bend affects the forces acting on it. A larger angle creates more force, as the fluid changes direction more drastically.

The force required to hold a bend in place is calculated using the momentum equation and considering the pressure forces and momentum changes within the bend.

The horizontal force exerted on a curved plate by a fluid jet is calculated by the change in the x-component of momentum of the fluid.

The vertical force on a curved plate due to a fluid jet is determined by the change in the y-component of momentum of the fluid.

The work done by a curved plate on a fluid jet is calculated by multiplying the force exerted on the fluid by the velocity of the plate.

The efficiency of a series of curved plates is the ratio of the output power (work done on the fluid) to the input power (power supplied to the plates).

The maximum efficiency of a series of curved plates occurs when the velocity of the fluid leaving the plates is half the velocity of the fluid entering the plates.

Energy losses occur in fluid flow through a sudden enlargement due to the conversion of kinetic energy to pressure energy, resulting in a pressure drop and energy loss.

Energy losses in sudden contractions are primarily due to the sudden expansion of the fluid jet after the contraction.

The coefficient of contraction (C_c) in a sudden contraction is the ratio of the cross-sectional area of the contracted jet to the area of the smaller pipe opening.

Energy losses occur in fluid flow through sharp bends due to separation of the flow from the bend surface, leading to turbulence and energy dissipation.

Forces on the fluid in sudden enlargement are determined by the change in momentum of the fluid, taking into account both the forces due to pressure and the forces from adjacent bodies.

The force exerted on a series of moving plates by a water jet is determined by the change in momentum of the water flowing through the plates, and the relative velocity between the water and the plates. It equals ρQ(v_in - v_out,n) where ρ is the density of water, Q is the flow rate, v_in is the water's initial velocity, and v_out,n is the water/plate's resultant velocity after striking the nth plate.

The power produced by a moving plate due to the water jet striking it is calculated by multiplying the force acting on the plate by its velocity. This represents the energy transfer rate from the water jet to the plate and is determined by the equation, Output Power = F_xv = ρQ[V-v]v, where ρ is the density of water, Q is the flow rate, V is the jet velocity, and v is the plate velocity.

The power supplied to a moving plate by a water jet is equal to the kinetic energy carried by the water jet. It represents the input power into the system and is given by the equation, Input Power = (1/2)mv² = (1/2)ρQV² = ρQV²/2, where ρ is the density of water, Q is the flow rate, and V is the jet velocity.

The efficiency of a moving plate is the ratio of the output power to the input power. It indicates how effectively the water jet's energy is converted into useful work by the plate. The efficiency equation is η = (Output Power)/(Input Power) = 2(V - v)v/V².

The maximum efficiency of a moving plate occurs when the plate's velocity (v) is half of the jet velocity (V). This means the efficiency is highest when the plate moves at half the speed of the water jet. It is found to be 50% or 0.5. This optimum velocity is given by V = 2v.

The horizontal force experienced by a fixed curved plate due to a water jet is determined by the change in momentum of the water in the x-direction as it strikes the plate. It is given by F_x = ρQ[v_in,x - v_out,x] = ρQ(V - Vcosθ) = ρa₁V(V - Vcosθ), where ρ is the density of water, Q is the flow rate, V is the jet velocity, θ is the angle of the plate, and a₁ is the plate's area.

The vertical force experienced by a fixed curved plate due to a water jet is determined by the change in momentum of the water in the y-direction as it strikes the plate. It is given by F_y = ρQ[v_in,y - v_out,y] = ρQ(0 - Vsindθ) = ρa₁V(0 - Vsindθ), where ρ is the density of water, Q is the flow rate, V is the jet velocity, θ is the angle of the plate, and a₁ is the plate's area.

The horizontal force experienced by a moving curved plate due to a water jet is determined by the change in momentum of the water in the x-direction as it strikes the plate. It is given by F_x = ρQ[v_in,x - v_out,x] = ρQ(v_r - v_rcosθ) = ρa₁V(v_r - v_rcosθ), where ρ is the density of water, Q is the flow rate, v_r is the relative velocity of the water jet and the plate, θ is the angle of the plate, and a₁ is the plate's area.