Kinematics of Fluid

Fluid kinematics: kinematics to review the position, velocity, and acceleration, not force.

In general, the fluid is known to have a tendency to move or flow. Very difficult to rein in the fluid so as not to move. Shear stress is very small already causing fluid to move. Similarly, an imbalance of the voltage (pressure) will normally cause the fluid to move. In this case we will consider a fluid with a fluid motion bernbagai aspects without reviewing the actual forces needed to produce movement., Meaning that we will review the kinematics of the movement., Velocity and acceleration of the fluid and the depiction and visualization of its movement.

1. MEDAN VELOCITY

In general, fluid flow, which means there is a net movement of molecules from one point to another in the space as a function of time.


Figure 1. The locus of a particle which is indicated by its position vector

Fluid parameters can be illustrated with a picture field. Thus, we can describe the flow of a fluid in motion of fluid particles, rather than describing for each molecule.

Fluid particles are very small tied together (as is assumed as a continuum). Thus, at a certain time, or the depiction of the fluid properties density, pressure, velocity and acceleration, can be given as a function and the spatial coordinates. Serving fluid parameters as a function of spatial coordinates is called the image field (fluid representation) of the flow. Of course, the picture of a particular field may be different at different times, so to describe a fluid flow we must determine the various parameters, not only as a function of spatial coordinates (eg x, y, z) but also as a function of time, t,. So for a complete state temperature, T = T (x, y, z, t), on the whole of the floor to the ceiling and from wall to wall at a time during day and night.

Variable one of the most important fluid is the velocity field:


where u, v, w are the components of velocity vector in the direction of x, y and z. By definition, the velocity of a particle is unity when the rate of change of the particle's position vector. Since the velocity is a vector, the velocity has the direction and magnitude.
Line-currents (Streamlines), Line-lined (Streakline), Line-trace (Pathlines)
Although the fluid motion can be very complicated, there are various concepts that can be used to help us visualize and analyze the flow field. Here we discuss the use of line-flow (streamline), line-lateral line (streakline) and line-trace (pathline) in the flow analysis. Line-currents are often used in analytic studies, while the line-trace of lateral line and the line is often used in experimental studies.

A flow line is a line everywhere offensive (Tangent of) the velocity field. If the steady flow, nothing has changed with time at a point (including the direction of the velocity), so the line-currents are fixed lines in space. For the flow is not steady, the line-current can change its shape over time. Line-currents obtained analytically by integrating equation offensive line velocity field. For two-dimensional flow, the slope of the line-currents, dy / dx, must be equal to the tangent of the angle of the velocity vector in accordance with the x-axis or:
If the velocity field is known as a function of x and y (and t if the flow is not steady (, then this equation can be integrated to obtain the equation of the line-currents.

For steady flow, the line-currents, line-lateral line, and lines are the same tracks.

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Bases of Bernoulli's Equation

Fluid flow past a blunt object will have a stagnation point in front of the body where the velocity is zero. The location of this point has a relatively large pressure and fluid flow divides into two parts, part flowing through the top and another across the bottom of the object.

Bernoulli's equation is an equation may be the most widely used in fluid mechanics. We will obtain Bernoulli's equation and apply them to different schools. Although this equation is one of the oldest in fluid mechanics and the assumptions used in very much lower, these equations can effectively be used to predict and analyze the flow situation. However, if the equation is applied without regard to the precise limits, serious errors can occur. Even this Bernoulli equation equation known as the most widely used and most widely misused in fluid mechanics.

1. Newton's Second Law

If a fluid particle moves from one place to another place, these particles usually experience an acceleration or deceleration. according to Newton's second law of motion, the net force acting on the particles under review should be equal to mass times acceleration: F = ma

Assumption fluid is inviscid, meaning: the fluid is assumed to have zero viscosity. If the viscosity is zero, then the thermal conductivity of the fluid is also zero and no heat transfer will occur (except by way of radiation). In practice there is no inviscid fluid, because in each of the fluid shear stresses arise when it imposed a strain rate of displacement. For most situations, the flow of the viscous effects of relatively small compared to other effects
Inviscid fluid flow is governed by the forces of pressure and gravity.

We assume that the fluid motion governed only by the forces of gravity and pressure and using Newton's second law is set at a fluid particle in the form of:

(net compressive force on a particle) + (net gravitational force on a particle) = (mass of particles) x (particle acceleration)


Fluid particles accelerated in the normal direction and along the stream.
As the particles move, the particle will follow a certain trajectory shape is determined by the speed of these particles. The locus of the particle along the trajectory is a function of where the particle was moving at the beginning and the velocity along the path. If the motion is a steady flow (steady flow), meaning no change according to time at a particular location in the flow field, each successive particles passing through a particular point such as point (1) in the image above will follow the same path. For this case, the path is a fixed line in the xz. Particles passing through adjacent sides of the point (1) will follow his own path, which may differ form the path that passes through the point (2), the entire field filled with xz trajectories were similar.
For steady flow (steady flow), each particle sliding along the trajectory and velocity vectors everywhere tangent to the path is. The lines that are tangent to the velocity vector field of flow around the so-called "flow lines (streamlines). Motion of particles is described in the distance s = s (t), along the line-current from a point of origin that is easy and the radius of local curvature of the line-current, R = R (t). The distance along the flow lines associated with the particle speed V = ds / dt, and the radius of curvature associated with the current form of the line. In addition to the coordinates along the line, s, is also the normal coordinates perpendicular to the flow line, n, as shown in the image above.

To apply Newton's second law on a particle current flowing along the line, we have to write according to the coordinates of the particle acceleration, the current line. By definition, acceleration is the rate of change of velocity with time of the particle, a = dV / dt. For two-dimensional flow in the xz, the acceleration has two components, a component along the line-currents, as the so-called downstream acceleration, and a normal component of flow lines, an, the so-called normal acceleration.

Downstream acceleration comes from the fact that the speed of the particles generally varies along the line-current, V = V (s). For example, in the picture above the rate of these particles may be 100 ft / s at the point (1) and 50 ft / s at the point (2).

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Contoh Perhitungan 2

Persoalan kedua :

Seorang pedagang meninggal dunia dan mempunyai harta waris sebanyak 24 juta rupiah. Dia meninggalkan istri, ibu, ayah, dan anak laki-laki. Maka berapakah bagian masing-masing ?

Dari persoalan di atas, maka jelas bahwa yang meninggal adalah seorang laki-laki. Dan untuk pembagianya adalah :

- Untuk istri, maka mendapatkan seper-delapan. Hal ini dikarenakan adanya far’un warits yakni anak laki-laki. Dan bagiannya menjadi 3 juta rupiah.

- Untuk ibu, maka mendapatkan seper-enam. Hal ini dikarenakan terdapatnya far’un warits yakni anak laki-laki. Dan bagiannya menjadi 4 juta rupiah.

- Untuk ayah, maka mendapatkan seper-enam. Hal ini dikarenakan terdapatnya far’un warits yakni anak laki-laki. Dan bagiannya menjadi 4 juta rupiah.

- Anak laki-laki, disini berkedudukan sebagai ‘ashobah yang artinya mendapatkan semua bagian yang tersisa. Sehingga untuk anak laki-laki memperoleh bagian terbanyak yakni 13 juta rupiah.

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Contoh Perhitungan 1

Persoalan pertama :

Seorang pengusaha meninggal dunia dan mempunyai harta waris sebanyak 10 juta rupiah. Dia meninggalkan suami, cucu perempuan, dan 3 saudara perempuan seibu. Maka berapakah bagian masing-masing ?

Dari persoalan di atas, maka jelas bahwa yang meninggal adalah seorang perempuan. Dan untuk pembagianya adalah :

- Untuk suami, maka mendapatkan seper-empat. Hal ini dikarenakan terdapatnya cucu perempuan yang dalam hal ini berkedudukan sebagai far’un waris.

- Untuk cucu perempuan, maka mendapatkan setengah. Hal ini dikarenakan tidak ada anak kandung, mu’ashib, serta mumaatsil bagi si mayit.

- Untuk 3 saudara perempuan seibu, maka tidak mendapatkan apa-apa. Hal ini dikarenakan mereka terhalang dengan adanya cucu perempuan yang berkedudukan sebagai far’un warits.

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Furuudul Muqoddaroh (lanjutan)

Seper-empat

a. Suami ; jika terdapat far’un warits bagi si mayit.
b. Istri ; jika tidak ada far’un warits bagi si mayit.

Seper-delapan

a. Istri atau istri-istri ; jika terdapat far’un warits bagi si mayit.

Dua-pertiga

a. Dua anak perempuan atau lebih ; jika tidak ada mu’ashib bagi keduanya.
b. Dua cucu perempuan atau lebih ; jika tidak ada anak kandung bagi si mayit dan juga tidak ada mu’ashib bagi keduanya.
c. Dua saudara perempuan sekandung atau lebih ; jika tidak ada far’un warits dan ashlu dzukur bagi si mayit, dan juga tidak ada mu’ashib bagi keduanya.
d. Dua saudara perempuan seibu atau lebih ; jika tidak ada far’un warits, ashlu dzukur, serta saudara sekandung bagi si mayit, dan juga tidak ada mu’ashib bagi keduanya.

Seper-tiga

a. Ibu ; jika tidak ada far’un warits dan tidak ada pula dua atau lebih dari saudara laki-laki atau saudara perempuan sekandung.
b. Dua atau lebih dari saudara laki-laki atau saudara perempuan seibu ; jika tidak terhalang.

Seper-enam

a. Ayah ; jika ada far’un warits bagi si mayit.
b. Kakek ; jika ada far’un warits bagi si mayit akan tetapi tidak terdapat ayah.
c. Ibu ; jika ada far’un waris dan juga dua atau lebih dari saudara laki-laki maupun saudara perempuan bagi si mayit.
d. Nenek ; jika tidak ada yang menghalangi.
e. Saudara laki-laki atau saudara perempuan seibu ; jika tidak terhalang.
f. Cucu perempuan ; jika ada satu anak perempuan guna menyempurnakan dua-pertiga.
g. Saudara perempuan sebapak ; jika ada saudara perempuan sekandung guna menyempurnakan dua-pertiga.

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