Question

Каждую 1 секунду в емкость поступает 5 кг воды. В дне бака есть круглое отверстие, через которое стекает вода. Уровень воды в баке находится на высоте h = 50 см от дна. Каков диаметр отверстия? плотность воды 1000 кг/м3?​

Answer 1

Дано:

t= 1 с

m= 5 кг

h =50 см=0,5 м

ρ=1000 кг/м3?​

Найти:D=?

Решение:

g=10 м/с^2

$D=\sqrt{\frac{m}{pi*p*t\sqrt{2g*h} } }=\sqrt{\frac{5}{3,14*1000*1\sqrt{2*10*0,5} } } =0,04 metra$

Answer 2

Calculation of the Diameter of the Hole

To calculate the diameter of the hole through which the water is flowing, we can use the principle of continuity, which states that the volume flow rate of a fluid is constant at any point in a closed system.

Given: - Water is flowing into the tank at a rate of 5 kg per second. - The water density is 1000 kg/m^3. - The water level in the tank is at a height of h = 50 cm from the bottom.

To find the diameter of the hole, we can use the following formula:

A1 * v1 = A2 * v2

Where: - A1 is the cross-sectional area of the tank at the water level (which is a circle). - v1 is the velocity of the water at the water level. - A2 is the cross-sectional area of the hole (also a circle). - v2 is the velocity of the water flowing through the hole.

We can calculate the cross-sectional area of the tank at the water level using the formula for the area of a circle:

A1 = π * r1^2

Where: - r1 is the radius of the tank at the water level.

To find the velocity of the water at the water level, we can use the equation:

v1 = Q / A1

Where: - Q is the volume flow rate of the water, which is equal to the mass flow rate divided by the density of water. - A1 is the cross-sectional area of the tank at the water level.

Now, let's calculate the diameter of the hole using the given information.

Calculation Steps:

Step 1: Convert the height of the water level from centimeters to meters: - h = 50 cm = 0.5 m

Step 2: Calculate the radius of the tank at the water level: - r1 = h = 0.5 m

Step 3: Calculate the cross-sectional area of the tank at the water level: - A1 = π * r1^2

Step 4: Calculate the volume flow rate of the water: - Q = mass flow rate / density of water - mass flow rate = 5 kg/s - density of water = 1000 kg/m^3 - Q = 5 kg/s / 1000 kg/m^3

Step 5: Calculate the velocity of the water at the water level: - v1 = Q / A1

Step 6: Calculate the cross-sectional area of the hole: - A2 = Q / v2

Step 7: Calculate the diameter of the hole: - diameter = 2 * √(A2 / π)

Let's perform the calculations:

Step 1: Convert the height of the water level from centimeters to meters: - h = 0.5 m

Step 2: Calculate the radius of the tank at the water level: - r1 = 0.5 m

Step 3: Calculate the cross-sectional area of the tank at the water level: - A1 = π * r1^2

Step 4: Calculate the volume flow rate of the water: - Q = 5 kg/s / 1000 kg/m^3

Step 5: Calculate the velocity of the water at the water level: - v1 = Q / A1

Step 6: Calculate the cross-sectional area of the hole: - A2 = Q / v2

Step 7: Calculate the diameter of the hole: - diameter = 2 * √(A2 / π)

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