Fluids

why do we incorporate surface pressure when calculating absolute pressure?

think of a lake, to find the pressure at the bottom of the lake we have to include both the pressure from the water of the lake and the atmosphere above (surface) exerts a pressure too (hydrostatic pressure = P₀ + pgh; P₀ not always 1 atm)

how the hydraulic lift shows pascal’s principle?

the tube on one side has SA₁ and a piston pushes down on the water for d₁ with F₁, on the other side, a tube with SA₂ has a piston pushed with force F₂ over d₂. the V displaced from tube 1 to tube 2 is the same. W = Fd, you apply a smaller force over a larger distance to exert a larger force

F₁/SA₁*(SA₁d₁) = F₂/SA₂*(SA₂d₂)

P₁V = P₂V (pressure is the same as it moves through the fluid and to the walls of the container)

Pascal’s principle

is an external pressure is applied to a confined fluid, the pressure at every point within the fluid and to the walls of the container increases by that amount

how is the pressure of the disk found at some height h in the tube?

the disk has Fnet = 0, so the down and up forces are the same. F_d = mg due to the liquid above the disk. mass of the liquid can be found from pV, F_d = pVg. V is determined by SA times h F_d = pSAhg. P = F/SA so P = phg

Why is there mercury that gets in the tube?

the space in the tube is a vaccum (no atm/P). there is 1atm of pressure on the mercury, so the mercury pushes 1 atm up into the tube (F net = 0). thus, the mercury in the tube has same pressure as 1 atm

how is net F acting on the block equal to its weight that was displaced?

the P at top is diff than the bottom (bottom is lower) so F_net = P_bx² - P_tx²

F_net = (pg(h+x) - pgh)x²

F_net = (pgh + pgx - pgh)x²

F_net = pgx³ = pgV = m_fluidg; the weight of the fluid displaced (same as block) is keeping it floating there; F_buoyancy > F_gravity

why is most of an iceberg submerged underwater?

ice has a specific gravity of 0.92 (p = 920 kg/m³) so about 92% of the ice will be submerged

why is density an intensive property?

because increasing the size of the object does not impact its density; increasing size increases both mass and volume (ratio stays same)

why do we say an object is ‘heavier’?

there are more atoms (has more mass) for the same amount of volume, making it more dense

density of water at 4C

1000kg/m³ or 1g/cm³ or 1g/mL

Block of wood has density of 130 kg/m³, what percent is submerged?

the forces must be equal since block is floating, so Fg = V(of block)p(of block)g

F_B= V(of submerged)p(of water)g

V_bp_bg = V_sp_wg

V_s/V_b = p_b/p_w

V_s/V_b = 130/1000 ×100

V_s/V_b = 13%

what is flux?

how much of something (volume) crosses a surface in some amount of time (V/t)

how is the continuity equation derived?

if some fluid is flowing through this tube, then the volume flowing in is equal to the volume flowing out. the distance the fluid moves in can be found by v_it, multiplied by area of tube opening gives volume = A_iv_it = A_ov_ot which equals to the output. therefore, A_iv_i = A_ov_o. this means that the mass of fluid flowing through the pipe at any point is the same

compare laminar and turbulent flow

laminar flow has little resistance because each fluid particle follows a smooth pathway which don’t cross with other particles

turbulent flow involves a lot more resistance because the fluid motion contains eratic, small circular currents (eddy currents)

explaining buoyant force between ball of water, racquet ball and billard ball all placed in the middle of a tub

the buoyant forces are all the same for each ball as their volumes are all the same (diff in pressures are the same, displaced water is the same) but the billard ball has a greater mass than the water, so its mg is greater than F_B making it sink, for the racquet ball its mass is less than water so the F_B is greater making it float (displaced water can keep it afloat)

equation for pressure

P = F(magnitude of normal force)/A (no direction)

conversions of Pa

1.013 × 10⁵ Pa = 760 mmHg = 760 torr = 1 atm

how a difference in pressure causes air to rush in and out of the lungs, windows to burst outward during a tornado etc.

when unequal pressures are exerted against objects, the forces acting on the object will add in vectors, could result in acceleration (a net force present). pressure on one side greater than the other

what is gauge pressure?

the difference between absolute pressure inside a tire for ex. and the atm pressure outside the tire. amount of pressure in a closed space above and beyond atm pressure

hydrostatics

the study of fluids at rest and the forces and pressures associated with standing fluids

a) 0.53m
b) 0.24m
c) 0.18m
d) 0.37m

b) 0.24m

Water is flowing through a pipe with a variable radius. Is pressure the same at the input and output of the pipe?

No, velocity of the water molecules change in different areas, meaning a net force (changing v means acceleration). plus, if the pipe goes uphill, pressure will decrease