Water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. in what time will the level of water in pond rise by 21 cm

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water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. in what time will the level of water in pond rise by 21 cm? what should be the speed of water if the rise in water level is to be attained in 1 hour?

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1. Time taken for water level to rise by 21 cm:

Answer:
To find the time taken for the water level to rise by 21 cm in the pond, we need to calculate the volume of water flowing from the pipe into the pond and then determine the time needed to achieve the desired rise.

Step 1: Calculate the volume of water flowing into the pond:

Given, the water is flowing at a rate of 15 km/h through a pipe of diameter 14 cm.
First, we need to find the area of the pipe’s cross-section:

Radius of the pipe, ( r = \frac{14}{2} = 7 \text{ cm} = 0.07 \text{ m} )
Area of the pipe’s cross-section, ( A = \pi r^2 = \pi \times (0.07)^2 )
Volume of water flowing per second, ( V = A \times 15000 \text{ m} = \pi \times 0.07^2 \times 15000 \text{ m} )

Step 2: Calculate the time for the water level to rise by 21 cm:

Given, the cuboidal pond is 50 m long, 44 m wide, and we want the water level to rise by 0.21 m (21 cm).
Volume of water required to raise the water level by 21 cm, ( V_{\text{required}} = 50 \times 44 \times 0.21 \text{ m}^3 )
Time taken to rise the water level, ( T = \frac{V_{\text{required}}}{V} )

Now, by calculating the above formula, we can find the time required for the water level to rise by 21 cm in the pond.

2. Speed of water to achieve the rise in 1 hour:

Answer:
If the rise in water level is to be attained in 1 hour, we can calculate the required speed of water flow.

Given, time taken is 1 hour (3600 seconds) and the required rise in water level is 21 cm (0.21 m).

Using the formula ( T = \frac{V_{\text{required}}}{V} ), we can rearrange it to find the speed of water flow as ( \text{Speed} = \frac{V_{\text{required}}}{T} ).

Substitute the values of ( V_{\text{required}} ) and 1 hour (3600 seconds) into the formula to obtain the speed of water needed to achieve the rise in the water level in one hour. Calculating this will provide the speed required for the water flow for the desired rise in the specified time.