9_Hydraulics Practice Quiz with Answer and Solution

Refresher - HYDRAULICS Quiz 9
PROBLEM 1:

A circular cone having a base diameter of 3.66 m and a height of 3.66 m,
connects to a circular cylinder of the same diameter and height of 3.66 m. The
assembly is filled with water with the cylinder vertically above the cone. An orifice
having an area of 0.0929 m2 is provided at the vertex of the cone, with the
coefficient of discharge C = 0.60.

➀ Estimate the time, in seconds, to empty the upper cylinder of its contents
through the orifice.
➁ Estimate the time, in seconds, to empty the lower right circular cone of its
contents through the orifice.
➂ Obtain the total time, in seconds, to empty the contents of the assembly.

Solution:
➀ Time to empty the upper cylinder of its contents through the orifice
3.66 m




t1 =
2 As ( h1 - h2 ) 3.66 m Cylinder
CA 2g

π(3.66)2 h1=7.32 m
As = = 10.52
4

t1 =
2(10.52) ( 7.32 - 3.66 ) h2=3.66 m Cone


0.60(0.0929) 2(9.81)

t 1 = 67.6 sec. A=0.0929 m2
C=0.60

, Refresher - HYDRAULICS Quiz 9
PROBLEM 1-3: cont.


➁ Time to empty the lower right circular cone of its contents through the orifice
By ratio and proportion
x 1.83
= 3.66 m
y 3.66 1.83 m
x = 0.5 y
3.66 A s dh
t2 = ∫ x
0
CA 2gh dh
3.66 m
As = π x2
y
A s = π(0.5y) 2



A s = 0.25 π y 2 A=0.0929 m2
C=0.60
3.66 A s dy
t2 = ∫
0
CA 2gy
0.25 π 3.66
t2 =
0.60(0.0928) 2(9.81)
∫
0
y 3/2 dy

3.66
3.18(2) ⎡⎣ y 5/2 ⎤⎦
t2 = 0
5
3.18(2)
t2 = ⎡(3.66)3/2 ⎤
5 ⎣ ⎦
t 2 = 32.6 sec.

➂ Total time to empty the contents of the assembly
t = t 1 + t2
t = 67.6 + 32.6 = 100.2 sec.