Do you understand volume flow rate? Determine the time required for a 50-L container to be filled with water when the speed of the incoming water is 25 cm/s and the cross-sectional area of the hose carrying the water is 3 cm2.

666.67 s

Explanation:

Q = AV ... (1)

Where Q=Volume of flow rate (m³/s), A=cross sectional area occupied by the flow rate (m²), V=Average velocity of flow (m/s).3

Give:A=3 cm²

and to convert from cm³ to m² (divide by 10000),

∴ A=3/10000=0.0003m²

And V=25cm/s

and to convert from cm/s to m/s (divide by 100),

∴V=25/100 (m/s) = 0.25m/s.

∴ Q=0.0003*0.25 = 0.000075m³/s.

Also, Q = V/t ... (2)

Where V=Volume of the container to be filled with water (m³)

t = Time take to fill the container (seconds).

making t, the subject of formula in equation 2,

t = V/Q

Given: V = 50L, to convert from L to m³ (divide by 1000)

∴V = 50/1000 = 0.05m³.

And Q=0.000075m³/s.

∴ t = 0.05/0.000075

⇒ t = 666.666667

approximating to 2 decimal place.

∴ t = 666.67 s