MOI UNIVERSITY
DEPARTMENT OF MECHANICAL & PRODUCTION ENGINEERING
MPE 232 : FLUID MECHANICS I
TUTORIAL 2
1. A venturimeter in a horizontal 300 mm diameter water pipe has a throat
diameter of 100 mm and a discharge coefficient of 0.98. A mercury U-tube is
used to measure the difference of head between the pipe inlet and the throat at
points 0.6 m apart. The mercury gauge reading is 760 mm, and the connections
to the U-tube are filled with water.
i) Determine the discharge through the pipe.
ii) The meter is now placed vertically with the flow upward. Determine the
gauge reading for the same rate of flow.
[106.2 dm3/s ; 760 mm]
2. The difference of level in a U-tube connected to the up- and down-stream
orifices of a pitot tube immersed in flowing water is 0.36 m, the specific of the
liquid 1.25, and the calibration coefficient for the orifices 0.865. Determine the
velocity in m/s. [0.813 m/s]
3. A swimming pool 40 m long and 15 m wide has vertical side walls. The depth of
water at the shallow end is 1 m and that at the deep end is 3 m. There are two
outlets, one at the bottom of each end. For each outlet, the cross-sectional area
is a = 0.3 m2 and Cd = 0.80. Find the time to empty the pool.
4. A thin rectangular plate 15 cm wide and 1 m long is immersed in glycerine and
is towed in the direction of its length at a constant speed of 1 m/s. Given for
glycerine, = 1260 kg/m3 and = 8.044x10-1 N-S/m2. Determine:
i) the coefficient of drag
ii) the boundary layer thickness at the trailing edge
iii) the shearing stress at the trailing edge
[0.033 ; 0.124 m ; 10.56 N/m2 ]
5. A thin plate 80 cm long and 15 cm wide moves at 3 m/s through water. The
boundary layer is 3 cm thick at the rear of the plate. The velocity distribution is
given by:
1
V y 2
V
Determine the resistance of the plate.
6. A pipe whose axis is horizontal is full of water in motion. At a section A the
velocity of water is 90 m/min and the pressure is 138 kN/m. If the pipe
gradually tapers from 150 mm diameter at A to 100 mm diameter at B,
determine the pressure of water at B, assuming that there is no loss of energy.
What must be the diameter of the pipe at B if the pressure there is reduced to
27.6 kN/m2 ? [133 kN/m2 ; 47.6 mm]
7. A fluid of constant density flows at the rate of 15 litres per second along a pipe
AB of 100 mm diameter. This pipe branches at B into two pipes BC and BD each
of 25 mm diameter and a third pipe BE of 50 mm diameter. The flow rates are
such that flow through BC is three times the flow rate through BE and the
velocity through BD is 4 m/s. Find the flow rates in the three branches AB, BC
and BE and the velocities in pipes AB, BC and BE.
[9.77 dm3/s ; 1.96 dm3 /s ; 3.26 dm3 /s ; 1.91 m/s ; 19.92 m/s ; 1.66 m/s]
2003/2004: prd232 - tutorial
DEPARTMENT OF MECHANICAL & PRODUCTION ENGINEERING
MPE 232 : FLUID MECHANICS I
TUTORIAL 2
1. A venturimeter in a horizontal 300 mm diameter water pipe has a throat
diameter of 100 mm and a discharge coefficient of 0.98. A mercury U-tube is
used to measure the difference of head between the pipe inlet and the throat at
points 0.6 m apart. The mercury gauge reading is 760 mm, and the connections
to the U-tube are filled with water.
i) Determine the discharge through the pipe.
ii) The meter is now placed vertically with the flow upward. Determine the
gauge reading for the same rate of flow.
[106.2 dm3/s ; 760 mm]
2. The difference of level in a U-tube connected to the up- and down-stream
orifices of a pitot tube immersed in flowing water is 0.36 m, the specific of the
liquid 1.25, and the calibration coefficient for the orifices 0.865. Determine the
velocity in m/s. [0.813 m/s]
3. A swimming pool 40 m long and 15 m wide has vertical side walls. The depth of
water at the shallow end is 1 m and that at the deep end is 3 m. There are two
outlets, one at the bottom of each end. For each outlet, the cross-sectional area
is a = 0.3 m2 and Cd = 0.80. Find the time to empty the pool.
4. A thin rectangular plate 15 cm wide and 1 m long is immersed in glycerine and
is towed in the direction of its length at a constant speed of 1 m/s. Given for
glycerine, = 1260 kg/m3 and = 8.044x10-1 N-S/m2. Determine:
i) the coefficient of drag
ii) the boundary layer thickness at the trailing edge
iii) the shearing stress at the trailing edge
[0.033 ; 0.124 m ; 10.56 N/m2 ]
5. A thin plate 80 cm long and 15 cm wide moves at 3 m/s through water. The
boundary layer is 3 cm thick at the rear of the plate. The velocity distribution is
given by:
1
V y 2
V
Determine the resistance of the plate.
6. A pipe whose axis is horizontal is full of water in motion. At a section A the
velocity of water is 90 m/min and the pressure is 138 kN/m. If the pipe
gradually tapers from 150 mm diameter at A to 100 mm diameter at B,
determine the pressure of water at B, assuming that there is no loss of energy.
What must be the diameter of the pipe at B if the pressure there is reduced to
27.6 kN/m2 ? [133 kN/m2 ; 47.6 mm]
7. A fluid of constant density flows at the rate of 15 litres per second along a pipe
AB of 100 mm diameter. This pipe branches at B into two pipes BC and BD each
of 25 mm diameter and a third pipe BE of 50 mm diameter. The flow rates are
such that flow through BC is three times the flow rate through BE and the
velocity through BD is 4 m/s. Find the flow rates in the three branches AB, BC
and BE and the velocities in pipes AB, BC and BE.
[9.77 dm3/s ; 1.96 dm3 /s ; 3.26 dm3 /s ; 1.91 m/s ; 19.92 m/s ; 1.66 m/s]
2003/2004: prd232 - tutorial
