Fluid Mechanics 1 Equations

Question 1

Streamlines (Field in u and v)

Answer 1

dx/u(x,y) = dy/v(x,,y)

Question 2

Pathlines (Field in u and v)

Answer 2

u(x,y,t) = dx/dt ; v(x,y,t) = dy/dt

Question 3

Viscous Stress (τ)

Answer 3

τ = μ * du/dy

Question 4

Hydrostatic Equation

Answer 4

dp/dz = -ρg

Question 5

Integrated Hydrostatic Equation (in terms of depth)

Answer 5

Δp = ρgΔh

Question 6

Hydrostatic Force on a surface

Answer 6

Fr = int(A) p(y) dA

Question 7

Moment of Hydrostatic Force

Answer 7

Mr = int(A) yp(y) dA

Question 8

Flow rate of quantity N

Answer 8

Ndot = int(A) ηρ u>.dA>

Question 9

Reynolds Transport Theorem

Answer 9

d/dt int(Vsys(t)) ηρ dV = d/dt int(CV) ηρdV + int(CS) ηρ u>.dA>

Question 10

Continuity Equation

Answer 10

d/dt int(CV) ρ dV + int(CS) ρ u>.dA> = 0

Question 11

Conservation of Momentum

Answer 11

d/dt int(CV) u> ρ dV + int(CS) u> ρ u>.dA> = sum(F>)

Question 12

Conservation of Momentum for Steady Flow

Answer 12

int(CS) uρ u>.dA> = sum(Fx)

Question 13

Conservation of Momentum for Steady flow and uniform velocity

Answer 13

mdot(u(out) - u(in)) = sum(Fx)

Question 14

Bernoulli Equation

Answer 14

p1/ρ + 1/2 * u^2 + gz = c

Question 15

Stagnation Pressure (p0)

Answer 15

p0 = p(inf) + 1/2 * ρ * u(inf)^2

Question 16

Pipe Flow Energy Equation

Answer 16

p1/ρg + 1/2g * u^2 + z = p2/ρg + 1/2g * u^2 + z + hL - hp

Question 17

Energy losses (hL)

Answer 17

hL = hf + hl

Question 18

Major Losses (hf)

Answer 18

hf = f * L/D * (u^2)/(2g)

Question 19

Minor Losses (hl)

Answer 19

hl = k * (u^2)/(2g)

Question 20

Pump Head (hp)

Answer 20

hp = Δp/ρg

Question 21

Poiseuille Flow (Between Plates)

Answer 21

u(y) = - (h^2)/2μ * ΔP/L * (1- (y^2)/(h^2))

Question 22

Hagen Poiseuille Flow (Round Pipe)

Answer 22

u(r) = - (R^2)/4μ * ΔP/L * (1-(r^2)/(R^2))