Fluid Mechanics and Styrofoam slab

[vmind]

Hi,

I really need help with the following two questions.



1.) A Styrofoam slab has a thickness of 3.8 cm and a density of 303

kg/m^3. When a 73.2 kg swimmer is resting on it, the slab floats

in fresh water with its top at the same level as the water surface.

What is the area of the slab?


2.) A horizontal pipe 18.0 cm in diameter has a smooth reduction to

a pipe 9.00 cm in diameter. If the pressure of the water in the

larger pipe is 9.00e4 Pa and the pressure in the smaller pipe is

6.00e4 Pa, at what rate does water flow through the pipes in kg/s?

 

[Doc Al]

Give these problems a try, show your work, and you'll get plenty of help.

Hint for #1: equilibrium
Hint for #2: Bernoulli

 

[vmind]

Hi,

I have tried the two problems and this is what I have so far.


1.) B(buyoancy)= mass of swimmer *g = p_water * v_displaced water * g

The weight of the slab = 303*(V_slab)*g = buyoancy of water

Then V_slab = (m*g)/(303*g)

V_slab = l*w*h

A_slab = V/h


2.) A_1 (big opening)= pi*(0.09)^2

A_2 (small opening) = pi*(0.0450)^2

A_1* v_1 = A_2 * v_2

v_2 = (A_1/A_2)* v_1

P_1+ 0.5pv_1^2 = P_2 + 0.5pv_2^2

P_1 - P_2 + 0.5p(v_1^2-(A_1/A_2)*v_1)=0


I am not sure how to find the rate of flow of water through

the pipes?

 

[Doc Al]

Problem #1: Think of all the forces that are acting on the "slab + swimmer". The weight of both act downward; this must be balanced by an upward force. The only upward force is the buoyant force which equals the weight of the volume of water displaced.

Problem #2: Solve that last equation for V₁. (The second V₁ should be V₁².) Once you have the speed, calculate the flow rate, which (volume/time) is A₁V₁. Use the density of water to get the flow rate in terms of mass.