Answer:
the proper diameter at its base so as to maintain the same volume flow rate is 1.6034 cm
Explanation:
Given the data in the question ;
flowrate Q = 400 cm³/s
cross section of the sprue is round
Diameter of sprue at the top d_top = 3.4 cm
Height of sprue = 20 cm = 0.2 m³
the proper diameter at its base so as to maintain the same volume flow rate = ?
first we determine the velocity at the sprue base
V_base = √2gh = √( 2×9.81×0.2) = √3.924 = 1.980908 m = 198.0908 cm
so, diameter of the sprue at the bottom will be
Q = AV = [ (( πd²_bottom)/4) × V_bottom ]
d_bottom = √(4Q/πV_bottom)
we substitute
d_bottom = √((4×400)/(π×198.0908 ))
d_bottom = √( 1600/622.3206)
d_bottom = √2.571022
d_bottom = 1.6034 cm
Therefore, the proper diameter at its base so as to maintain the same volume flow rate is 1.6034 cm
