Hydrology and Hydraulics: Venturi Meter, Pump Efficiency, and Hydrograph

Surname 1
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Hydrology and Hydraulics
Question 1
The pressure drop in a Venturi meter varies only with the fluid density, velocity of approach and
the diameter ratio of the meter. Venturi meter 1 in water at 250C shows a 10kPa drop when the
approach velocity is 6m/s. Meter 2, geometrically similar to meter 1, is used in a 0.15M3/s flow
of kerosene (density = 800kg/m3).
i. Use the Buckingham pi method to develop the governing relationship
ii. Find the upstream pipe diameter that will yield 20kPa drop in meter 2.
Solution
Given that
n=5 and independent quantities are 3 that is (D, V and Density)
But using the buckingham pi theorem
3.14=3.14 (f ( D ,V , density , P))
This equals D a V b c (ML−1T −2)
(L)a(¿−1)b(ML−3)c (ML−1 T −2)=3.14
But it is established that a+ b−3 c=1
Solving for a, b and c we obtain (Thompson p.20)
-b-2=0
c=-1
b=-2
a=0
But the Function is given as = /( V2)
(b)

Surname 2
Given that At T= 25C, V=6m/s and P1=10 kPa
Additionally, Q=0.15m3/sec and P2=20 Kpa
But the function is given as
P m/(m V m2)=P p /( p V p 2)
10000/(997 X 6 x 6)=20000/(800 xV 2)
V=9.47m/sec
But also flow rate discharge Q= AxV
0.15=0.785 xDxDx 9.47
D=0.14m
Question 2
Water is being pumped from a lower reservoir to an elevated tank as shown below. The pump is
80% efficient and rated at 200kW. Determine the flow rate if the total head loss from point 1 to 2
is 15m.
Solution
Given that Z1= 50m, Z2 = 100m and h2 = 15m