# Pertemuan Minggu 3 : 28 Februari & 3 Maret 2023

CATATAN PERKULIAHAN

Gaya Hidrostatis

Gaya hidrostatis adalah gaya yang timbul akibat tekanan hidrostatis pada suatu fluida terhadap suatu benda yang terendam dalam fluida tersebut. Gaya hidrostatis dinyatakan dalam persamaan:

F = ρghA

di mana: F adalah gaya hidrostatis yang dihasilkan oleh fluida pada suatu benda ρ adalah densitas (massa jenis) fluida g adalah percepatan gravitasi bumi h adalah kedalaman benda terhadap permukaan fluida A adalah luas permukaan benda yang terkena tekanan hidrostatis

Dari persamaan tersebut, dapat dilihat bahwa gaya hidrostatis bergantung pada densitas fluida, kedalaman benda, dan luas permukaan benda yang terkena tekanan hidrostatis. Semakin dalam kedalaman benda dan semakin besar luas permukaan benda yang terkena tekanan hidrostatis, maka semakin besar pula gaya hidrostatis yang dihasilkan oleh fluida pada benda tersebut.

```                                                                F = P.A
```
```                                                              F = ρ.g.h.A
```

Dikarenakan densitas dan percepatan gravitasi bersifat konstan, maka :

```                                                               F = γ.h.A

```

Untuk menggerakkan pintu air, diperlukannya momen. Momen adalah kemampuan benda atau komponen untuk bergerak terhadap poros atau titik pusat benda tersebut. Besar momen merupakan perkalian antara gaya dan jarak gaya ke titik pusat.

```                                                                M = F.d
```

Resultan gaya pada momen tersebut memilki titik yang terletak pada titik pusat tekanan. Lalu, untuk mencari koordinat atau posisi titik pusat tekanan (Center of Pressure) diperlukan untuk mengetahui nilai inersia dari material yang digunakan, misal :

I=1/12 bh^3

I=1/4 πr^4

Gaya Apung

Gaya apung merupukana perwujudan dari hukum Archimedes yang mengatakan bahwa setiap benda yang sebagian atau seluruhnya terendam dalam zat cair, atau sebagian zat cair, mempunyai gaya dorong ke atas pada benda tersebut, atau yang sering disebut gaya apung. Di dalam hukum Archimedes atau pada gaya apung, berlaku kesetimbangan gaya pada setiap koordinat, tetapi lebih spesifik pada sumbu y. Berdasarkan hal tersebut, didapatkan persamaan gaya apung sebagai berikut :

```                                                               F = ρ.g.V
```

```                                                                CHATGPT
```

1). Hidrostatis resultant force for hydrostatic force in water gate

The resultant force for hydrostatic force in a water gate is the net force acting on the gate due to the pressure of the water on it. This force is typically calculated using the principles of hydrostatics, which describe the behavior of fluids at rest.

In general, the hydrostatic force acting on a submerged surface is given by the equation:

```                                                              F = γAdepth
```

where F is the hydrostatic force, γ is the specific weight of the fluid (the weight per unit volume), A is the area of the submerged surface, and depth is the depth of the fluid above the surface.

For a water gate, the hydrostatic force acting on the gate will depend on the depth of the water above the gate, the area of the gate that is submerged, and the specific weight of water. To calculate the resultant force, we would need to determine the total hydrostatic force acting on the gate, taking into account any variations in depth or pressure across the surface of the gate.

The resultant force is simply the vector sum of all the individual hydrostatic forces acting on the gate. It will have both magnitude and direction, and will be equal and opposite to the force exerted by the gate on the water.

In practice, the design and operation of water gates typically take into account the hydrostatic forces acting on them to ensure that they can withstand the forces and operate safely and efficiently.

Hydrostatic force on a flat surface refers to the pressure exerted by a fluid on a flat surface that is submerged in it. The hydrostatic force depends on the depth of the fluid and the density of the fluid.

When a flat surface is submerged in a fluid, each point on the surface experiences the same hydrostatic pressure exerted by the fluid around it. The hydrostatic pressure on a flat surface can be calculated using the following formula:

```                                                               P = ρgh
```

where: P is the hydrostatic pressure on the surface (in units of Pa or N/m^2) ρ is the density of the fluid (in units of kg/m^3) g is the acceleration due to gravity (in units of m/s^2) h is the depth of the fluid above the surface (in units of m)

For a flat surface that is completely submerged in a fluid, the hydrostatic force can be calculated by multiplying the hydrostatic pressure by the area of the surface:

```                                                               F = PA
```

where: F is the hydrostatic force exerted on the surface (in units of N) A is the area of the surface (in units of m^2)

The direction of the hydrostatic force is perpendicular to the surface, and it always acts upwards, opposing the weight of the fluid above the surface. The magnitude of the hydrostatic force on a flat surface increases with the depth of the fluid and the area of the surface, and it can be used to calculate the stability of submerged objects or the strength of structures that are designed to withstand hydrostatic forces.

Hydrostatic force on buoyancy refers to the upward force exerted by a fluid on a submerged object, which is also known as the buoyant force. This force is equal to the weight of the fluid that is displaced by the object and acts in the opposite direction to the weight of the object.

The buoyant force is a result of the pressure exerted by the fluid on the submerged object. The pressure at any point in a fluid is proportional to the depth of the fluid above that point. Therefore, the pressure on the bottom of a submerged object is greater than the pressure on the top of the object, and this pressure difference creates an upward force on the object.

The magnitude of the buoyant force is determined by the volume of the fluid that is displaced by the submerged object, which is known as the displaced volume. The displaced volume is equal to the volume of the object that is submerged in the fluid, and it can be calculated using the dimensions of the object and the depth of the fluid.

The buoyant force can be calculated using the following formula:

```                                                F_buoyancy = ρ_fluid * g * V_displaced
```

where: F_buoyancy is the buoyant force exerted on the object (in units of N)

ρ_fluid is the density of the fluid (in units of kg/m^3)

g is the acceleration due to gravity (in units of m/s^2)

V_displaced is the displaced volume of the fluid (in units of m^3)

The buoyant force is a crucial concept in the design of ships, submarines, and other submerged structures. It is also used in the design of flotation devices and life jackets to keep people afloat in water.