Answer:
It takes him 751.39 seconds to fill the trough
Explanation:
The flow rate = Velocity of the hose × cross sectional area of the hose.
Q = V×A................................... Equation 1
Where Q = flow rate, V = velocity, A = cross sectional area.
Given: V = 1.66 m/s,
A =πd²/4, Where d = 2.00 cm = 0.02 m.
Therefore, A = 3.143(0.02)²/4 = 0.0003143 m²
Substituting these values into equation 1
Q = 1.66×0.0003143
Q = 0.0005217 m³/s.
Time taken to fill the trough = Volume of the trough/flow rate.
t = V/Q.......................................... Equation 2.
Where V = volume of the trough, Q = flow rate.
Given: Q = 0.0005217 m³/s, V = length×width×height = l×w×h, l = 1.53 m, w = 61 cm = 0.61 m, h = 42 cm = 0.42 m.
V = 1.53×0.61×0.42 = 0.392 cm³
Substituting these value into equation 2,
t = 0.392/0.0005217
t = 751.39 seconds.
Thus it takes him 751.39 seconds to fill the trough
The time taken for the cowboy to fill the ranch is 12.53 min.
The given parameters;
The volume of the ranch is calculated as follows;
V = Lwh
V = 1.53 x 0.61 x 0.42
V = 0.392 m³
The area of the hose is calculated as follows;
[tex]A = \pi r^2 \\\\A = \pi \times (0.01)^2\\\\ A= 0.000314 \ m^2[/tex]
The volumetric flow rate of the water is calculated as follows;
Q = Av
[tex]\frac{V}{t} = Av\\\\t = \frac{V}{Av} \\\\t = \frac{0.392}{0.000314 \times 1.66} \\\\t = 752.1 \ s\\\\t = 12.53 \min[/tex]
Thus, the time taken for the cowboy to fill the ranch is 12.53 min.
Learn more here:https://brainly.com/question/13254954
