Estimate the speed of the water free surface and the time required to fill with water a cone-shaped container 1.5 m high and 1.5m across at the top if the filling rate is 75.7 L/min.

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

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

Hence,

so, the speed of water surface at height h

where,

is 75.7 L/min = 0.0757m³/min

h = 1.5m

so,

v = 0.04283 /60

v = 0.0007138m/s

Hence, speed of water is 0.0007138m/s

1 a

2 b

3 b

4 d

5 d

6 d

explanation: