A circular dam has a radius of 10.0 m and a height of 3.0 m. Of the dam will be filled with water from a pipe with an inside diameter of 10 cm and a water flow of 10 litres per second, calculate the time taken to fill the dam to a point 10 cm from the top of the dam.
All you need is the volumetric flow rate (10L/s) and the volume pi r^2 h.
convert L to m^3
Time=Volume/Rate (t=v/Q)
Where Volume is V=r^2h
●V=(10)^2(3)
=300m^3
●Q=10/1000=0.01m^3/s
●T=v/Q
=300/0.01
=30000sec...
To calculate the time taken to fill the dam to a certain height, we need to find the volume of water that needs to be filled and then divide it by the flow rate.
Step 1: Calculate the volume of the portion of the dam that needs to be filled.
Given that the dam is circular with a radius of 10.0 m and a height of 3.0 m, we need to find the volume of a cylinder with those dimensions. The formula to find the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height.
V = π(10.0)^2(3.0) = 300π m^3
Step 2: Convert the volume from cubic meters to liters.
1 cubic meter is equal to 1000 liters, so we multiply the volume by 1000.
300π m^3 × 1000 L/m^3 = 300000π L
Step 3: Find the height at which we want to stop filling the dam.
The dam's total height is 3.0 m, and we want to fill it up to a point 10 cm from the top. Convert 10 cm to meters: 10 cm ÷ 100 cm/m = 0.1 m
Step 4: Calculate the volume of the portion of the dam we want to fill.
The formula to find the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height.
V = π(10.0)^2(3.0 - 0.1) = 900π - 9π = 891π m^3
Step 5: Convert the volume from cubic meters to liters.
891π m^3 × 1000 L/m^3 ≈ 2818838.06 L
Step 6: Calculate the time taken to fill the dam.
The flow rate is given as 10 liters per second, so we divide the volume we need to fill by the flow rate.
Time = Volume ÷ Flow rate
Time = 2818838.06 L ÷ 10 L/s ≈ 281883.806 seconds
So, it will take approximately 281883.806 seconds to fill the dam to a point 10 cm from the top.