Answer:
It will take him 763.68 s to fill the trough
Step-by-step explanation:
Flow rate,
V = Qt ........... Equation 1
Where Q = flow rate, V = volume, t = time
making t the subject of equation 1
t = V/Q............... Equation 2
But,
Q = Av.................... Equation 3
Where A = area, v= velocity.
Given: v = 1.5 m/s, and
A = πd²/4 where d = 2.0 cm = 0.02 m, π = 3.143
A = 3.143(0.02)²/4
A = 0.0003143 m³
Substituting these values into equation 3,
Q = 1.5×0.0003143 = 0.0004714 m³/s
Also, V = lbw.................. Equation 4
Where l = length, b = width, w = width.
given: l = 1.5 m, b = 40 cm = 0.4 m, w = 60 cm = 0.6 m.
Substituting these values into 4,
V = 1.5×0.4×0.6
V = 0.36 m³.
using Equation 2,
t = V/Q
Where V = 0.36 cm³, Q = 0.0004714 m³/s
therefore,
t = 0.36/0.0004714
t = 763.68 s
Therefore it will take him 763.68 s to fill the trough