Problems

Student’s name …............................................ group …………. Data……..

#1. A cube of iron 0.300 m on a side is suspended (in equilibrium) from a large spring scale (which reads in Newtons) held over a giant tank of water. The center of the cube is 30.00 m below the surface of the water.

(a)What is the volume of the cube?

(b) What is the mass of the cube?

(c) What is the weight of the water displaced by the cube?

(d) What is the magnitude of the force of buoyancy on the cube?

(e) What is the reading on the spring scale ?

(f) What is the pressure on the top surface of the cube?

(g) What is the pressure on the bottom surface of the cube?

(h) What is the force on the top surface of the cube?

(i) What is the force on the bottom surface of the cube?

(j) What is the difference between the force on the bottom and the force on the top?

2.  A piece of lead has the shape of a hockey puck, with a diameter of 7.5 cm and a height of 2.5 cm. If the puck is placed in a mercury bath it floats. How deep below the surface of the mercury is the bottom of the lead puck?

3.A liquid flows through a pipe with a diameter of 10 cm at a velocity of 9cm/s. If the diameter of the pipe then decreases to 6 cm, what is the new velocity of the liquid?

4. The rate of flow of water through a horizontal pipe is 0.24 m3 /min. what is the velocity of flow at a point where the diameter of the pipe is 7 centimeter and 0.4 centimeters?

5. The volume flow rate of water through a horizontal pipe is 3.9 m3/min. Determine the speed of flow (in m/s) at a point where the diameter of the pipe is 16.8 cm. Enter a number with two digits behind the decimal point.

6. A tank of water releases its water through a small hole near the bottom of a tank. If the difference between the top of the water and the hole is 180cm, what is the velocity of the water as it escapes the tank?

7.

8. Through a refinery, fuel ethanol is flowing in a pipe at a velocity of 1 m/s and a pressure of 101300 Pa. The refinery needs the ethanol to be at a pressure of 2 atm (202600 Pa) on a lower level. How far must the pipe drop in height in order to achieve this pressure? Assume the velocity does not change. (Hint: Use the Bernoulli equation. The density of ethanol is 789 kg/m3 and gravity g is 9.8 m/s2. Pay attention to units!)

 9. А pump forces water at a constant flow rate out through a pipe whose cross-sectional area gradually decreases. At the exit point, the cross-sectional area, A₂, is 1/3 the cross-sectional area at the entrance, A₁. If the difference between the entrance and exit heights is equal to 60cm, and the flow speed just after the the water leaves the pump is 1m/s, what is the gauge pressure (or pressure minus that due to the atmosphere) at the entrance point?

10. Water at a gauge pressure of 3.8 atm at street level flows in to an office building at a speed of 0.06 m/s through a pipe 5.0 cm in diameter. The pipes taper down to 2.6cm in diameter by the top floor, 20 m above. Calculate the flow velocity and the gauge pressure in such a pipe on the top floor. Assume no branch pipe and ignore viscosity.

11.   On Fig. 1, draw streamlines to illustrate laminar flow round the object shown.

                                                                                                        Fig. 1

Fig.2

12. The large piston in a hydraulic lift has a radius of 250 cm2 . What force must be applied to the small piston with a radius of 25 cm2 in order to raise a car of mass 1500 kg?

13. When the button of a trash compactor is pushed, a force of 350 N pushes down on a 1.3 cm2 input piston, creating a force of 22,076 N to crush the trash. What is the area of the piston that crushes the trash?

14. Johnny the auto mechanic is raising a 1200 kg car on her hydraulic lift so that she can work underneath. If the area of the input piston is 12 cm2 , while the output piston has an area of 700 cm2 , what force must be exerted on the input piston to lift the car?