CE3201
Advanced Fluid Mechanics
Lecture-12
Impact of a Water Jets
Module:
Impulse Momentum
Equation and its
Applications
Sequence
• Flow through nozzle
• The momentum equation
• Force exerted by flowing fluid on a pipe bend
• Force of jet striking normally to a stationary
flat plate
• Force of jet striking a plate moving with a
uniform velocity
Flow Through Nozzles
Flow Through Nozzles
Flow Through Nozzles
The Momentum Equation
Force exerted by Flowing Fluid on a
Pipe Bend
Force exerted by Flowing Fluid on a
Pipe Bend
Numerical Problems
Numerical Problems
Force of jet striking normally to a
stationary flat plate
Let a jet of dia ‘d’ sticking a stationary flat plate as
shown in the fig.
A is the area of the jet and Q is the discharge of the
jet.𝝆 is the density of the fluid. The impulse force can
be obtained by impulse momentum equation.
Force of jet striking normally to a
stationary flat plate
𝛴𝐹 = 𝝆𝑄 𝑣2 − 𝑣1
After striking with stationary plate fluid comes in
rest so v2=0
The above equation becomes
𝛴𝐹 = 𝝆𝑄 0 − 𝑣1
𝛴𝐹 = −𝝆𝑄𝑣
Since 𝑄 = 𝐴𝑣
𝛴𝐹 = −𝝆𝐴𝑣 2
𝛾 2
𝛴𝐹 = − 𝐴𝑣
𝑔
Impact of Jet 13
Force of jet striking normally to a
stationary flat plate
From the equation it is observed that for a given
fluid force is directly proportional to square of
the velocity of striking jet.
𝐹𝝰𝑣 2
Example:
Find out the force of jet on a stationary plate,
discharge of jet is 0.0589 m3/s and velocity of jet
is 30m/s.
Impact of Jet 14
Numerical Problems
Example:
Find out the force of jet on a stationary plate,
discharge of jet is 0.0589 m3/s and velocity of jet is
30m/s.
From the IMP
𝛴𝐹 = −𝝆𝑄𝑣 or F=denxity x volume/t xvelocity or F= Mass flow rate x V
Here
𝝆=1000 kg/m3 Q=0.0589m3/s v=30m/s
𝐹 = 1000𝑥0.0589𝑥30 = −𝟏𝟕𝟔𝟕 𝑵
Impact of Jet 15
Force of jet striking a plate moving
with a uniform velocity
• Consider a fluid jet striking a flat plate held
normal to the direction of motion of the jet and
moving with uniform velocity u away from the jet
• Velocity of the plate is usually less than the
velocity of the jet otherwise the jet will not strike
the plate
• The effective velocity of the jet will be the one
with which the jet is approaching the plate and
will be the relative of the two
Force of jet striking a plate moving
with a uniform velocity
• Relative velocity with which the jet strikes the
plate is given by (𝑣 − 𝑢)
• The mass flow rate for the case of moving plates
is given by
𝑚/𝑡 = 𝜌𝐴(𝑣 − 𝑢)
The force on the jet is given by
𝑚
𝐹= 𝑥𝑉 (impulse momentum eq)
𝑡
Putting the values in above equation we get
𝐹 = 𝜌𝐴(𝑣 − 𝑢) 2
Impact of Jet 17
Force of jet striking a plate moving
with a uniform velocity
• For the case of moving plates, work is done on
the plate by the jet so if W is the work done
per unit time then
• W=force x distance moved by the plate per
unit time
𝑊 = 𝐹. 𝑑 = 𝜌𝐴(𝑣 − 𝑢)2 . 𝑑
Impact of Jet 18
Assignment Problems
Problem 1
A 1-in dia jet has a velocity of 95 fps. Calculate the resultant fore on a large flat plate if
this jet were to strike it normally.
Problem 2
A 40 mm dia jet has a velocity of 25 m/s. if this jet were to strike a large flat plate
normally, what would be the resultant force on the plate.
