Water flows from a circular pipe of diameter 3.5cm into a rectangular tank 66cm long,35cm wide and 45cm high. If it takes 18 minutes to fill the tank completely, determine the rate of flow of the water in the pipe?
(66*35*45 cm^3)/18min = 5775 cm^3/min
volume of the tank =66×35×45
=103,950cm^3
rate= 103950cm^3/18 min
=5775cm^3/min
To determine the rate of flow of water in the pipe, we need to calculate the volume of water that flows into the tank in 18 minutes.
Step 1: Calculate the volume of the tank:
The volume of a rectangular tank can be calculated using the formula: volume = length × width × height.
Given the dimensions: length = 66 cm, width = 35 cm, and height = 45 cm, we can calculate the volume as follows:
volume = 66 cm × 35 cm × 45 cm = 103,950 cm³.
Step 2: Convert the volume from cm³ to liters:
1 liter is equal to 1000 cm³. So, we can convert the volume to liters as follows:
volume = 103,950 cm³ ÷ 1000 = 103.95 liters.
Step 3: Calculate the flow rate:
The flow rate is defined as the volume of fluid passing through a given section per unit time. In this case, the flow rate is the volume of water that flows into the tank in 18 minutes.
flow rate = volume ÷ time = 103.95 liters ÷ 18 minutes.
Step 4: Convert the flow rate from liters/minute to cm³/minute:
1 liter is equal to 1000 cm³. So, we can convert the flow rate as follows:
flow rate = 103.95 liters ÷ 18 minutes = 103,950 cm³ ÷ 18 minutes.
Therefore, the rate of flow of water in the pipe is 5,775 cm³/minute.
To determine the rate of flow of the water in the pipe, we need to find the volume of water that flows into the tank per unit time.
First, let's calculate the volume of the tank:
Volume of the tank = length × width × height
= 66 cm × 35 cm × 45 cm
Next, we need to convert the units of time from minutes to seconds since the diameter of the pipe is given in centimeters:
18 minutes = 18 × 60 seconds
Now, let's calculate the cross-sectional area of the pipe:
The diameter of the pipe is given as 3.5 cm, which means the radius is half of the diameter, so the radius of the pipe is 3.5 cm ÷ 2 = 1.75 cm.
The cross-sectional area of the pipe can be calculated using the formula for the area of a circle:
Cross-sectional area = π × (radius)²
Now, let's calculate the volume of water that flows into the tank per second:
Volume per second = Cross-sectional area × velocity
Finally, to find the rate of flow of the water in the pipe, we divide the volume per second by the time it takes to fill the tank completely.
Let's calculate the values step by step:
Step 1: Calculate the volume of the tank
Volume of the tank = 66 cm × 35 cm × 45 cm
Step 2: Convert the units of time
18 minutes = 18 × 60 seconds
Step 3: Calculate the cross-sectional area of the pipe
Cross-sectional area = π × (1.75 cm)²
Step 4: Calculate the volume of water that flows into the tank per second
Volume per second = Cross-sectional area × velocity
Step 5: Calculate the rate of flow of the water in the pipe
Rate of flow = Volume per second ÷ Time taken to fill the tank completely
By following these steps and plugging in the values, you will be able to determine the rate of flow of the water in the pipe.