GIVEN:

L = 3.0 cm = 0.03 m

r = 0.3 mm = 0.0003 m

(delta) y = 1.0 m

1 pint = 500 cm^3 [approx.] given

a) Find the rate of flow, F = ?
b) How long will it taken to inject 1 point of blood,
t = ?

a & b) I know we need to find the pressure or speed.

F = (P at) (A) = (P at ) (pie) r^2

F = (1.01E5 Pa)(0.3 m)^2 (?)

? = I'm thinking to include 0.03 m and just put
(0.3 m)(0.03 m)

(delta) p = (density, roy) g (delta) h

I'm pretty sure we should use density of the blood

P1 - P2 = 8 (pie) n (multiply) vL/A

I'm trying every equation and can't see to get the right answer. But I know we need to have either speed or pressure to find the other and then we can be able to find time. I really need help on this one problem, thank you very much for any help

I'm wondering if I use this equation

v = (square root) (2gh) and then find the pressure and time

To find the rate of flow, F, and the time it will take to inject 1 pint of blood, t, we need to find the pressure or speed first. Let's go step by step:

Step 1: Calculate the area, A, of the given cross-section:
A = πr^2 (where r is the radius of the cross-section)

Given that r = 0.0003 m, we can calculate A:
A = π(0.0003 m)^2
A = 2.827E-7 m^2

Step 2: Calculate the pressure difference, ΔP, using the formula:
ΔP = ρgh (where ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height difference)

Given that h = 1.0 m, we need the density of blood to calculate ΔP. Let's assume the density of blood is ρ = 1060 kg/m^3 (typical value).

ΔP = (1060 kg/m^3)(9.8 m/s^2)(1.0 m)
ΔP = 10388 Pa

Step 3: Calculate the flow rate, F, using the formula:
F = ΔP × A

F = (10388 Pa)(2.827E-7 m^2)
F ≈ 2.937E-3 kg/s

So, the rate of flow is approximately 0.002937 kg/s.

Step 4: Convert the given volume of blood to cubic meters:
1 pint ≈ 500 cm^3 ≈ 0.0005 m^3

Step 5: Calculate the time, t, using the flow rate, F, and the given volume of blood:
t = Volume / F

t = 0.0005 m^3 / 0.002937 kg/s
t ≈ 0.170 s

Therefore, it will take approximately 0.17 seconds to inject 1 pint of blood.

Note: The equation v = √(2gh) you mentioned is the equation for the velocity of fluid flow under the influence of gravity. It is not directly applicable to this problem since we don't have the velocity of the fluid. Instead, we calculated the pressure difference and then used the area of the cross-section to find the flow rate and time.