Question

Біля підніжжя водонапірної вежі висотою 40 м зірвало водопровідний кран. Діаметр утвореного отвору 6 см. З якою силою потрібно притискали заглушку до отвору, щоб не лилася вода? Дати розгорнуту відповідь (дано, СІ і тд.)

Answer 1

Ответ:

1130 Н

Объяснение:

h=40м

d=6cм=0,06 м

g=10м/с2

р=1000кг/м3

Сила тиску визначається за формулою: F=PS

Тиск стовпа рідини визначається за формулою: P=pgh

Площа становить: S=$\frac{\pi d^{2} }{4}$

Підставляємо все у першу формулу: F=$\frac{pgh\pi d^{2} }{4}$

F=$\frac{1000 *10*40*3,14*0,06^{2} }{4}$=1130 Н

Answer 2

Calculation of the Force Required to Seal the Hole

To calculate the force required to seal the hole in the water pipe, we can use the principles of fluid mechanics. The force required to prevent water from flowing out of the hole is equal to the pressure of the water multiplied by the area of the hole.

The pressure of the water can be calculated using the formula:

Pressure = Density × Gravity × Height

Where: - Density is the density of water, which is approximately 1000 kg/m^3. - Gravity is the acceleration due to gravity, which is approximately 9.8 m/s^2. - Height is the height of the water column above the hole, which is equal to the height of the water tower minus the depth of the hole.

In this case, the height of the water column above the hole is equal to the height of the water tower, which is 40 m.

The area of the hole can be calculated using the formula:

Area = π × (Radius)^2

Where: - π is a mathematical constant approximately equal to 3.14159. - Radius is half the diameter of the hole, which is 6 cm.

Now let's calculate the force required to seal the hole.

Calculation Steps:

1. Convert the diameter of the hole from centimeters to meters: - Diameter = 6 cm = 0.06 m

2. Calculate the radius of the hole: - Radius = Diameter / 2 = 0.06 m / 2 = 0.03 m

3. Calculate the area of the hole: - Area = π × (Radius)^2 = 3.14159 × (0.03 m)^2 ≈ 0.0028274 m^2

4. Calculate the pressure of the water: - Pressure = Density × Gravity × Height = 1000 kg/m^3 × 9.8 m/s^2 × 40 m ≈ 392000 Pa (Pascal)

5. Calculate the force required to seal the hole: - Force = Pressure × Area = 392000 Pa × 0.0028274 m^2 ≈ 1107.5 N (Newton)

Therefore, the force required to seal the hole and prevent water from flowing out is approximately 1107.5 Newtons.

Please note that this calculation assumes ideal conditions and does not take into account factors such as friction or the elasticity of the material used to seal the hole.