Question

1. A “bed of nails” is a huge number of nails arranged in a piece of wood so that they all point up with the sharp points vertically upward. A person can lay down on the “bed of nails” and rest on these thousands of nails without pain or injury. Explain how this can occur.

2. A huge battleship is made of steel which has a density close to iron (almost ten times that of water) yet it can float. Explain why.

3. When a fluid flows through a constriction in a pipe, does the pressure in the fluid increase, decrease of remain constant. Explain your answer fully.

4. A large tank full of water has a nozzle which is open and water shots out of the nozzle vertically. The calculated speed of efflux of water is , which means the water fountain should rise as high as the upper surface of the water as it drains from the tank. In reality, does this actually happen. Justify your answer.

5. What is the difference between pressure and stress, if any? Explain including the units for each.

1. On a day when the atmospheric pressure is, a diver at the bottom of a fresh water lake at a depth of 26m finds a open glass tube (closed a the bottom) containing an unknown liquid (density = 5.6 g/cm3) which is 1.75 m deep. What is the absolute pressure at the bottom of the unknown liquid?

2. A rectangular shaped dam is 460m deep and 1000m wide. It holds fresh water. What is the total force due to water pressure on the dam?

3. A rectangular block of plastic (density = 3.00 x 102 kg/m³) if dimensions l = 25.0 cm, w = 15.0 cm and h = 12.0 cm is placed in water. A) What volume of the block is submerged? B) A metallic (volume 15.0 cm³) block is now placed on top of the plastic block so that the water level is exactly at the top of the plastic block. What is the density of the metallic block?

4. A fluid flows through a horizontal circular pipe that widens, making a 45^o angle with the y axis as shown below. The thin part of the pipe has radius 3 cm and the speed of the fluid is .15 m/s . If the x axis has origin at the point where the pipe widens, what is the speed of the fluid when x= 10 cm?

5. Liquid toxic waste with a density of 1752 kg/m3 is flowing through a section of pipe with a radius of 0.312m at a velocity of 1.64 m/s. a) what is the velocity of the waste after it goes through a constriction and enters a second section of pipe at a radius of 0.222m? b) If the waste is under a pressure of 850,000 Pa in the first section of pipe, what is the pressure in the second section? c) If the second section of pipe flowing horizontally turns to vertical, how high would the fluid have to rise so that the pressure decreases by 50%?

6. Water is flowing in a pipe has a diameter at point A of 8.00 cm tapering to 3.50 cm at point B. Point B is 12.0 cm below point A. The water pressure at point A is 3.20 x 10⁴ Pa and decreases by 50% at point B. Assume steady, ideal flow. What is the speed of water at point A? What is the speed of the water at point B?

7. Calculate the atmospheric pressure in pascals if the height of a mercury column in a barometer is 760 mm. The density of mercury is 13.6 x 10³ kg/m³.

8. What fraction of an iceberg is above water when floating in fresh water? Assume the density of the iceberg is 917 kg/m³.

9. A cylindrical tank of height 0.40 m is open at the top and has a diameter of 0.16m. It is filled with water (assume it to be an ideal fluid, no viscosity) up to a height of 0.16m. Find the time it takes to empty the tank through a hole of radius 5.0 x 10^-3 m in the bottom of the tank.

10. In a hydraulic lever, the cross sectional areas of the pistons are 0.250 m² and 1.00 m². We minimum amount of force that must be applied to the smaller piston to support a car of mass 1200 kg that is resting on the larger piston?

Answer 1

1. It is the force per unit are( i.e Pressure ) on the skin that determines if a nail will pierce it. If one single nail is used, the entire weight of the body is exerted on that single nail tip ( which has a very small surface area ), which results in a massive pressure which is likely going to pierce the skin. On the other-hand when we have hundreds of nails ( more the better ), in this scenario the weight of the body is now distributed across all these hundreds of nail tips. This results in decreasing the effective pressure exerted on the exposed skin. This value of pressure is equal on all nail tips ( they all need to be at same level ) which is quite less than the value required to pierce the skin, hence a person can conveniently lie on the bed of nails without any injury.

2. A massive piece of steel which has density greater than water will definitely sink in water, but in-case of a battleship. The battleship is actually a massive structure which is hollow, what it means that although the mass of the ship remains same but since the metal is spread to encompass a hollow space its net volume increases, which subsequently reduces its effective density. The ships are constructed such that this effective density becomes lesser than that of water and hence buoyant force keeps the ship afloat.

3. To explain this we need just only 2 laws and its associated expression.

Firstly equation of continuity which suggest that rate of volume flow of water remains same, i.e

Thus if A₂ is lesser than A1 then subsequently v2 is greater than v1.

Nest we take aid of Bernoulli's Law for pressure.

Therefore provided H1=H2 i.e the are at same level, from previous expression we see v2 is greater than v1

To compromise this we see that P2 is lesser than P1.

Thus, if a fluid passes into a constricted region, its pressure decreases.