Chapter 3 Fluid Dynamics (Fluid Kinematics). ME804306-2 Fluid Mechanics. Dr. Kamel Mohamed Guedri Mechanical Engineering Department, The College of Engineering and Islamic Architecture, Umm Al- Qura University, Room H1091 Website: https://uqu.edu.sa/kmguedri Email: email@example.com.
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Dr. Kamel Mohamed Guedri
Mechanical Engineering Department,The College of Engineering and Islamic Architecture,
Umm Al-Qura University, Room H1091
Website: https://uqu.edu.sa/kmguedriEmail: firstname.lastname@example.org
3.1 Uniform Flow, Steady Flow
uniform flow:flow velocity is the same magnitude and direction at every point in the fluid.
non-uniform:If at a given instant, the velocity is not the same at every point the flow. (In practice, by this definition, every fluid that flows near a solid boundary will be non-uniform - as the fluid at the boundary must take the speed of the boundary, usually zero. However if the size and shape of the of the cross-section of the stream of fluid is constant the flow is considered uniform.)
steady: A steady flow is one in which the conditions (velocity, pressure and cross-section) may differ from point to point but DO NOT change with time.
unsteady:If at any point in the fluid, the conditions change with time, the flow is described as unsteady. (In practice there is always slight variations in velocity and pressure, but if the average values are constant, the flow is considered steady.)
3.2 Mass and volume flow rate
1. The law of conservation of matter
3. The law of conservation of momentum
(density of fluid,) (volume of fluid entering per second Q)
Q (entering) = Q (leaving)
Q (entering) = Q (leaving)(3.5a)
Q (entering) = V1 A1
Q (leaving) = V2A2
V1A1 = V2A2(3.5b)
1 A1V1= 2 A2V2
(m: mass, V: velocity, h: height above the datum).
mgz1 + mV12 = mgz2 + mV22
V12 + gz1 = V22 + gz2
mgz1 = ½ mV22 + mgz2
mg ( z1 - z2 ) = ½ mV22
V2 = (3.8)
3.4 Application of Bernoulli Equation
or the velocity through the orifice,
Further refinement of the value could be obtained by a new calculation of V1 (0.0681 m3/s 0.26 m2), a new calculation of H + V12/2g and so on. One correction is usually sufficient, however, to give a value of Q acceptable to three significant figures.
3.6.1 The force due the flow around a pipe bend
Why do we want to know the forces here? Because the fluid changes direction, a force (very large in the case of water supply pipes,) will act in the bend. If the
bend is not fixed it will move and eventually break at the joints. We need to
know how much force a support (thrust block) must withstand.
3.6.2 The force on a pipe nozzle
Force on the nozzle at the outlet of a pipe. Because the fluid is contracted at the nozzle forces are induced in the nozzle. Anything holding the nozzle (e.g. a fireman) must be strong enough to withstand these forces.
3.6.3 Impact of a Jet on a plane
We will first consider a jet hitting a flat plate (a plane) at an angle of 90 o, as shown in the figure below. We want to find the reaction force of the plate i.e. the force the plate will have to apply to stay in the same position.