Answer:
speed of water is 0.0007138m/s
Explanation:
From the law of conservation of mass
Rate of mass accumulation inside vessel = mass flow in - mass flow out
so, dm/dt = mass flow in - mass flow out
taking p as density
[tex]d \frac{dQ}{dt} = pq_i_n[/tex]
where,
q(in) is the volume flow rate coming in
Q = is the volume of liquid inside tank at any time
But,
dQ = Adh
where ,
A = area of liquid surface at time t
h = height from bottom at time t
A = πr²
r is the radius of liquid surface
[tex]r = (1.5/2) \div 1.5[/tex] [tex]h = \frac{h}{2}[/tex]
Hence,
[tex]\pi( \frac{h}{2} )^2\frac{dh}{dt} =q_i_n[/tex]
[tex]\frac{dh}{dt} = \frac{q_i_n}{\pi (\frac{h}{2})^2 } =\frac{4q_i_n}{\pi h^2}[/tex]
so, the speed of water surface at height h
[tex]v = \frac{dh}{dt} =\frac{4q_i_n}{\pi h^2}[/tex]
where,
[tex]q_i_n[/tex] is 75.7 L/min = 0.0757m³/min
h = 1.5m
so,
[tex]v = \frac{4 \times 0.0757}{\pi \times 1.5^2} \\\\v = 0.04283m/min[/tex]
v = 0.04283 /60
v = 0.0007138m/s
Hence, speed of water is 0.0007138m/s
