Equation of continuity Definition and 16 Threads

Consider a fixed horizontal tube of uniform cross section with pressure being 1atm at one of it's end and 5atm at the other (former due to 'open to atmosphere' and latter due to force on a piston), then liquid would flow towards low pressure end. By equation of continuity all cross sections will...

Hi there, So I was doing the dishes this morning using a sink wand hat can toggle between different flow speeds. The way that I've always thought of this working is using the equation of continuity: Volume flow rate: = Area*velocity Pressing a button on the wand decreases the cross-sectional...

Homework Statement You are watering your lawn with a hose when you put your finger over the hose opening to increase the distance the water reaches. If you are pointing the hose at the same angle, and the distance the water reaches increases by a factor of 4, what fraction of the hose opening...

The equation states that A1V1=A2V2. What about in a situation like a showerhead, where it's one long pipe/tube, then opens up to say, 20 holes. Is it now A1V1=A2V2/20 ? why/why not?

I'm really confused by this question, as it is different than the examples we did in class. I've compared my answer with a few classmates and I'm getting a different one, so I'm not sure if I've done it wrong or if they have. I'd really just like to know if I am on the right track! Thank you :)...

Hi all, I'm considering an fluids example that's giving me an apparent contradiction when I consider it from the perspective of Bernoulli's Equation vs. the Equation of Continuity. What I'm thinking of is the common observation that putting one's thumb over a garden hose results in an increase...

How does equation of continuity relate to conservation of mass principle? Laymans terms please.

Suppose their is a bucket with water inside it and there is a small hole at the bottom of the bucket such that water leaks from the end. Area of cross section of the bucket is A and area of the small hole is a. The velocity with which water is coming out of the hole is v and the velocity with...

Hey there, I trying to understand the following coordinate transformation of the equation of continuity (spherical coordinates) for a vaporizing liquid droplet\frac{\partial \rho}{\partial t} + \frac{1}{r^2} \frac{\partial}{\partial r} (r^2 \rho v) = 0 into \epsilon \sigma \frac{\partial...

Homework Statement A large vertical cylindrical rainwater collection tank of cross sectional area A is filled to a depth h. The top of the tank is open and in the centre of the bottom of the tank is a small hole of cross sectional area B (B<<A). Derive expressions for (i) the flow speed...

Homework Statement A can of height h and cross-sectional Area Ao is initially full of water. A small hole of area A1<<Ao is cut in the bottom of the can. Find an expression for the time it takes all the water to drain from the Can. Hint: Call the water depth y use the continuity equation to...

Homework Statement I am looking to demonstrate that the expressions for the charge and current density of point charges satisfy the equation of continuity of charge. Intuitively it makes sense to me but I run into trouble with the delta function when I try to prove it mathematically.Homework...

π²³ ∞ ° → ~ µ ρ σ τ ω ∑ … √ ∫ ≤ ≥ ± ∃ · θ φ ψ Ω α β γ δ ∂ ∆ ∇ ε λ Λ Γ ô Homework Statement Show that Lorentz' gauge equation ∇.A = -µ(jωε+σe)φ is the equation of continuity ∇ .Ji = (jωε+σe)/ε P(R) Homework Equations The Attempt at a Solution I tried taking curl, div of...

Homework Statement A water line with an internal radius of 6.1*10^-3 m is connected to a shower head that has 24 holes. The speed of the water in the line is 1.2 m/s. (b) At what speed does the water leave one of the holes (effective radius = 4.6*10^-4 m) in the head...

Homework Statement Use the Schrodinger Equation to show that \frac{\partial}{\partial t}(\Psi^{*} \Psi) = - \underline{\nabla}. \underline{j} Homework Equations \underline{j} = \frac{-i}{2m} \left[\Psi^{*}(\nabla \Psi) - (\nabla \Psi^{*})\Psi]\right \frac{\partial}{\partial...

Homework Statement A liquid with a specific gravity of 0.9 is stored in a pressurized, closed storage tank to a height of 7 m. The pressure in the tank above the liquid is 8700 Pa. What is the intial velocity of the fluid when a 5 cm valve is opened at a point 0.5 m from the bottom of the...