1. Water is pumped at a constant velocity 1m/s from large reservoir resting on the floor to the open top of an absorption tower. The point of discharge is 4 meter above the floor, and the friction losses from the reservoir to the tower amount to 30 J/kg. At what height in the reservoir must the water level be kept if the pump can develop only60 J/kg?
2222112f 1U P U P w=Z g+h (Z g+)22ρρ
++-+ U 1=0 12P =P 10Z = W=60j/kg f h 30/kg =
2U =1m/s 2(60300.5)/g 3m Z =--=
21Z Z Z 431m ∆=-=-=
2. The fluid (density 1200 kg/m 3 ) is pumped at a constant rate 20 m 3 /h from the large reservoir to the evaporator. The pressure above the reservoir maintains atmosphere pressure and the pressure of the evaporator keeps 200 mmHg (vacuum). The distance between the level of liquid in the reservoir and the exit of evaporator is 15 meter and frictional loss in the pipe is 120 J/kg not including the exit of evaporator, what is the pump effective work and power if the diameter of pipe is 60 mm?
22112212f U U Z g+W Z g+h 22
ρρP P ++=++ 10P = 5422200P x1.013x10 2.67x10N /m 760
=-=- 31200Kg /m ρ= 1U 0= f h 120J /kg =
22V 20U 1.97m /s A 3600*4006
===π/*. 1Z 0= 2Z 15= 42
2.67x101.97W 15x9.81120246.88J /kg 12002
=-+++= N W Q 246.88x1200x20/3600=1646W ρ==
3. Water comes out of the pipe (Φ108x4 mm), as shown in Fig. The friction loss of the pipeline which does not cover the loss at the exit of pipe can be calculated by the following equation:
h f =6.5U 2
where U is the velocity in the pipe, find
a. water velocity at section A-A'.
b. water flow rate, in m 3 /h.
22112212f U U Z g+
Z g+h 22ρρP P +=++ 1U 0= 12P =P 1Z 6m = 2Z 0=
2f h 6.5U = 2
2U 6x9.81 6.5U 2
=+ U 2.9m/s = 23V=UA=2.94x01
x360082m /h =π/.
4. Water passes through the variable pipe. The velocity in the small pipe is 2.5 m/s. The vertical glass tubes are inserted respectively at the section A and B to measure the pressure (see fig.) If the friction loss between two section is 15 J/kg, what is the water column difference between two glass tubes? By the way, draw the relative liquid column height of two tubes in the Fig.
a a
b b U A U A = 2b U 2.5*(33/47)1.23m /s == 22a a b b a b f U U Z g+Z g+h 22
ρρP P +=++ a b Z =Z 22a b b a f U U h 22
ρρP P -=-+221.23/2 2.5/21512.63=-+= a b P P R g ρ-=∆ 3312.63R=1.29x10m 9.8x10
-∆=
5. A centrifugal pump takes brine (density 1180 kg/m 3 , viscosity 1.2 cp) from the bottom of a supply tank
and delivers it into another tank. The line between the tanks is 300 m of 25 mm diameter pipe (inner diameter). The flow rate is 2 m 3 /h. In this line, there are two gate valves, four elbows (90o ) and one return bend, what is the friction loss if the roughness of pipe is 0.025 mm?
22
f fst flocal U U h h h 4f k d 22
l ∑=+=+∑ 31180kg /m ρ= 300m, d=0.025m l =
3-3v 2m /h =1.2cp=1.2x10Pa.s μ=
k=0.025mm k/d=0.025/25=0.001
c l r k =0.4 k =1 k =2x0.07=0.14
el re k 4x0.75 3 k 1.5-2.2===
2u v /A 2/(3600x /4x0.025)1.13m /s π===
4u d Re 2.78x10ρμ
== f 0.063= 2f 2h 4x0.0063x300/0.025x1.13/2+
(0.4+1+2x0.07+4x0.7+1.5)x1.13/2 =197.86J/kg
∑=
6. The orifice meter (diameter of orifice 0.0001 m) is installed for measuring the flow rate. The indicating liquid of orifice is mercury if U shape pressure gauge reading is 0.6 meter and orifice coefficient can be taken
as 0.61, what is the flow rate of water?
o u c =
20o 0V u s 0.61x /4x0.0001π==
835.8x10m /s -=
7. Water flows through a pipe with a diameter di 100 mm as shown in figure.
a. when the valve is closed, R is 600 mm and h equals 1500 mm. While the valve opens partially, R=400 mm and h=1400 mm, f=0.00625 (Finning factor) and k c =0.5 (contraction coefficient), what is the flow rate of water, in m 3 /h?
b. If the valve opens fully, what is the pressure of section 2-2', in N/m 2 ? The equivalent length of the valve is
1.5 m and the Fanning factor f keeps the same?(ρH2O =1000kg/m 3, ρHg =13600kg/m 3)
