UNIVERSITY OF SANTO TOMAS
Faculty of Engineering
Department of Mechanical Engineering
Problem Set 1
Solve the following problems.
1. A viscometer, used to measure the viscosity of a liquid, is composed of two 12-cm-long
concentric cylinders with radii 4 and 3.8 cm. The outer cylinder is stationary and the inner
one rotates. If a torque of 0.046 N·m is measured at a rotational speed of 120 rpm, estimate
the viscosity of the liquid. Neglect the contribution to the torque from the cylinder ends and
assume a linear velocity profile.
2. Air at 22 °C is received from the atmosphere into a 200 cm3 cylinder. Estimate the
pressure and temperature if it is compressed isentropically to 10 cm3.
3. Determine the depth of a liquid needed to create a pressure difference of 225 kPa if the
liquid is (a) water, (b) mercury, and (c) oil with SG = 0.86.
4. Calculate the pressure difference between the air pipe and the water pipe in
5. Determine the new differential reading along the inclined leg of the mercury manometer
if the pressure in pipe A is decreased 10 kPa and the pressure in pipe B remains unchanged.
The fluid in A has a specific gravity of 0.9 and the fluid in B is water.
6. A homogenous, 4-ft wide, 8-ft long, rectangular gate weighing 800 lb is held in place by
a horizontal flexible cable as shown. Water acts against the gate which is hinged at point
A. Friction in the hinge is negligible. Determine the tension in the cable.
7. A 4-m long curved gate is located in the side of a reservoir containing water as shown.
Determine the magnitude and direction of the force of the water on the gate.
8. A closed tank is filled with water and has a 4-ft diameter hemispherical dome as shown.
A U-tube manometer is connected to the tank. Determine the vertical force of the water on
the dome if the differential manometer reading is 7 ft and the air pressure at the upper end
of the manometer is 12.6 psi.
9. The homogenous timber AB is 0.15 m by 0.35 m in cross section. Determine the specific
weight of the timber and the tension in the rope.
10. A 1-m diameter cylindrical mass, M, is connected to a 3-m wide rectangular gate as
shown. The gate is to open when the water level, h, drops below 2.5 m. Determine the
required value for M. Neglect friction at the gate hinge and the pulley.