A 5/8 inch (inside) diameter garden hose is used to fill a round swimming pool 7.3m in diameter.How long will it take to fill the pool to a depth of 1.0m if water issues from the hose at a speed of 0.50m/s ?

V(pool) =π•D²•h/4

V= π•d²•vt/4
π•D²•h/4= π•d²•vvt/4
t=D²vh/d²•v

t = volume/(volume flow rate)

= (pi/4)*D^2*(depth)/ [(pi/4)*d^2*V]
= (D/d)^2*(depth)/V

d is the hose diameter. D is the pool diameter.
V is the water velocity leaving the hose.

To find out how long it will take to fill the pool to a depth of 1.0m, we need to calculate the volume of water that needs to be transferred.

1. First, let's convert the inside diameter of the hose from inches to meters.
5/8 inch = 0.625 inch
1 inch = 0.0254 meters (approx.)
Therefore, the inside diameter of the hose in meters is:
0.0254 meters x 0.625 = 0.015875 meters

2. Now, we can calculate the cross-sectional area of the hose, using the formula for the area of a circle:
Area = π * (radius)^2
Radius = diameter / 2
Radius = 0.015875 meters / 2 = 0.0079375 meters
Area = π * (0.0079375)^2 = 0.0001981635 square meters

3. Next, we need to calculate the volume of water flowing from the hose per second. We know the speed of the water is 0.50 m/s, and the cross-sectional area is 0.0001981635 square meters.
Volume = speed * area
Volume = 0.50 m/s * 0.0001981635 square meters = 0.00009908175 cubic meters/s

4. The volume of water needed to fill the pool to a depth of 1.0m can be found using the formula for the volume of a cylinder:
Volume = π * (radius)^2 * height
Radius = diameter / 2
Radius = 7.3m / 2 = 3.65m
Volume = π * (3.65)^2 * 1.0m = 41.88759996 cubic meters

5. Finally, we can calculate the time it will take to fill the pool by dividing the volume of water needed by the volume of water flowing per second.
Time = Volume / Rate
Time = 41.88759996 cubic meters / 0.00009908175 cubic meters/s
Time ≈ 423.1581545 seconds

Therefore, it will take approximately 423.16 seconds or 7 minutes and 3 seconds to fill the pool to a depth of 1.0m.

To calculate the time it will take to fill the pool to a depth of 1.0m using a 5/8 inch diameter garden hose, we need to follow these steps:

Step 1: Convert the diameter of the garden hose to meters.
The diameter of the garden hose is given in inches, so we need to convert it to meters. Since there are 2.54 centimeters in one inch, we can calculate the diameter of the garden hose in meters as follows:

Diameter in meters = (5/8) * 2.54 / 100

Step 2: Calculate the cross-sectional area of the garden hose.
The cross-sectional area of the garden hose can be calculated using the formula:

Area = π * (radius^2)

Since the diameter of the garden hose is given, we can calculate the radius by dividing it by 2:

Radius = Diameter / 2

Step 3: Calculate the volume of water flowing out of the hose per second.
The volume flow rate can be calculated using the formula:

Volume Flow Rate = Area * Velocity

Step 4: Calculate the time it will take to fill the pool.
The time can be calculated using the formula:

Time = Volume / Volume Flow Rate

Now, let's calculate:

Step 1:
Diameter in meters = (5/8) * 2.54 / 100 = 0.01619 meters (rounded to 5 decimal places)

Step 2:
Radius = Diameter / 2 = 0.01619 / 2 = 0.00809 meters

Area = π * (radius^2) = π * (0.00809^2) = 0.0002067 square meters (rounded to 7 decimal places)

Step 3:
Volume Flow Rate = Area * Velocity = 0.0002067 * 0.50 = 0.00010335 cubic meters per second (rounded to 8 decimal places)

Step 4:
Pool Volume = π * (radius^2) * depth = π * (7.3/2)^2 * 1 = 10.619 cubic meters (rounded to 3 decimal places)

Time = Volume / Volume Flow Rate = 10.619 / 0.00010335 ≈ 102,779 seconds

Therefore, it will take approximately 102,779 seconds to fill the pool to a depth of 1.0m using a 5/8 inch diameter garden hose.