MOMENTUM TRANSFER PROBLEMS
FLUID STATICS AND OVER-ALL MASS AND ENERGY BALANCE
(Midterm Assign#1)
1. An oil is being pumped inside a 10.0-mm diameter pipe at a Reynolds number of 2100.
The oil density is 855 kg/m3 and the viscosity is 2.1 x 10-2 Pa-s. (a) What is the velocity in
the pipe? (b) It is desired to maintain the same Reynolds number of 2100 and the
same velocity as in part (a) using a second fluid with a density of 925kg/m3 and a viscosity
of 1.5 x 10-2 Pa-s. What pipe diameter should be used?
2. A hydrocarbon liquid enters a piping system an average velocity of 1.282 m/s, where A1 =
4.33 X 10- 3 m2 and ρ1 = 902 kg/m3. The liquid is heated in the process and the exit density
is 875 kg/m3. The cross-sectional area at point 2 is 5.26 x 10-3 m2. The process is steady
state. (a) Calculate the mass flow rate at the entrance and exit. (b) Calculate the average
velocity v in 2 and the mass velocity G in 1.
3. Water at 93.3°C is being pumped from a large storage tank at 1 atm abs at a rate of
0.189m3/min by a pump. The motor that drives the pump supplies energy to the pump at
the rate of 1.49 kW. The water is pumped through a heat exchanger, where it gives up 704
kW of heat and is then delivered to a large open storage tank at an elevation of 15.24 m
above the first tank. What is the final temperature of the water to the second tank? Also,
what is the gain in enthalpy of the water due to the work input?
4. A turbine operates under steady flow conditions, receiving steam at the following state:
pressure 1200 kPa, temperature 1880C, enthalpy 2785 kJ/kg, speed 33.3 m/s and elevation
3 m. The steam leaves the turbine at the following pressure 20 kPa, enthalpy 2512 kJ/kg,
speed 100 m/s, elevation 0 m. Heat is lost to the surroundings at the rate of 0.29 kJ/s. If,
the rate of steam flow through the turbine is 0.42 kg/s, what is the power output of the
turbine in kW?
MECHANICAL ENERGY BALANCE AND FLOW-METERING DEVICE
(Midterm Assign#2)
1. Soybean oil is being pumped through a uniform-diameter pipe at a steady mass-flow rate.
A pump supplies 209.2 J/kg mass of fluid flowing. The entrance abs pressure in the
inlet pipe to the pump is 103.4 kN/m2. The exit section of the pipe downstream from the
pump is 3.35 m above the entrance and the exit pressure is 172.4 kN/m2. Exit and entrance
pipes are the same diameter. The fluid is in turbulent flow. Calculate the friction loss in the
system. Density of soybean oil is 919 kg/m3.
2. A pump pumps 0.200 ft3/s of brine solution having a density of 1.15 g/cm3 from an open
feed tank having a large cross-sectional area. The suction line has an inside diameter of
3.548 in. and the discharge line from the pump a diameter of 2.067 in. The discharge flow
goes to an open overhead tank and the open end of this line is 75 ft above the liquid level
in the feed tank. If the friction losses in the piping system are 18.0 ft-lbf/lbm, what pressure
must the pump develop and what is the horsepower of the pump if the efficiency is 70%?
The flow is turbulent.
3. Water having a density of 998 kg/m3 is flowing at the rate of 1.676 m/s in a 3.068-in.diameter horizontal pipe at a pressure of 68.9 kPa abs. It then passes to a pipe having an
inside diameter of 2.067 in. (a) Calculate the new pressure P2 in the 2.067-in. pipe. Assume
no friction losses. (b) If the piping is vertical and the flow is upward, calculate the new
pressure P2. The pressure tap for P2 is 0.457 m above the tap for P1.
4. Water is being pumped from an open water reservoir at the rate of 2.0 kg/s at 10oC to an
open storage tank 1500 m away. The pipe used is schedule 40 3 in. pipe and the frictional
losses in the system are 625 J/kg. The surface of the water reservoir is 20 m above the level
of the storage tank. The pump has an efficiency of 75%. (a) What is the kW power required
for the pump? (b) If the pump is not present in the system, will there be a flow?
5. Water at 20°C is flowing in a 2-in. schedule 40 steel pipe. Its flow rate is measured by a
venturi meter having a throat diameter of 20 mm. The manometer reading is 214 mm of
mercury. The venturi coefficient is 0.98. Calculate the flow rate.
MECHANICAL ENERGY BALANCE WITH FRICTIONAL LOSSES
(Finals Assign.)
1. Hot water in an open storage tank at 82.2°C is being pumped at the rate of 0.379 m3/min
from this storage tank. The line from the storage tank to the pump suction is 6.1 m of 2-in.
schedule 40 steel pipe and it contains three elbows. The discharge line after the pump is 61
m of 2-in. pipe and contains two elbows: The water discharges to the atmosphere at a height
of 6.1 m above the water level in the storage tank. (a) Calculate all frictional losses. (b)
Make a mechanical-energy balance and calculate Ws of the pump in J/kg. (c) What is the
kW power of the pump if its efficiency is 75%?
2. Water is pumped from a reservoir to a storage tank atop a building by means of a centrifugal
pump. There is a 200-ft difference in elevation between the two water surfaces. The inlet
pipe at the reservoir is 8 ft below the surface, and the local conditions are such that level is
substantially constant. The storage tank is vented to the atmosphere and the liquid level is
maintained constant. The inlet pipe to the storage tank is 6 ft below the surface. The piping
system consists of 200 ft of 6 in sch 40 steel pipe containing two 900 elbows and one open
gate valve from the reservoir to the pump; 6-in pipe follows the pump for a length of 75 ft
after which the pipe size is reduced to 4-in sch 40 steel pipe for 250 ft to the tank. The 4in pipe contains one gate valve and three 900 elbows. It is desired to maintain the flow of
water into the tank of 625 gpm. Water temperature is 680F. If the pump-motor set has an
overall efficiency of 60%, what would be the pumping costs be in dollars per day if
electricity costs $ 0.08 per kW-hr?
3. A horizontal tubular type of boiler uses crude oil consisting substantially of hydrocarbons.
Th oil is available at 700F and has a specific gravity of 8.90 and viscosity of 58 cP. In actual
operation, water is fed to the boiler at a temperature 600F and vaporized to form steam at a
gauge pressure of 100 psi and 98% quality of steam at a steam generation rate of 10 lb of
steam per lb of oil fired. The average analysis of the flue gases is as follows: CO 2 = 11%;
CO = 0.5%; O2 = 6%; and N2 = 82.5%. At normal running rate the boiler generates 3450
lb of steam per hour. (a) If the boiler water is available from a well 30 ft below the feed
line and the water line consists of 200 ft (total and equivalent) of 1-in standard steel pipe,
what horsepower pump should be used if the efficiency of the pump is only 50%? (b) The
oil feed comes from a reservoir under a suitable head. The feed line consists of standard
3/4 in steel pipe. A properly made pitot tube is inserted at the center line of the pipe and its
leads are filled with oil and attached to a vertical U-tube, containing both oil and water. At
normal running rate what differential in water level should be maintained? (c) Air is
available at 800F and is substantially dry. The line consists of 50 ft of 6-in standard steel
pipe. The air is supplied to the furnace by means of centrifugal fan, direct driven by a
motor. Motor efficiency is 90% and fan efficiency is 35%. What size motor should be used?