continuity equation

The velocity field of a two-dimensional, incompressible flow is given by V⃗ = 2 sinh x î + v(x, y) ĵ where î and ĵ denote the unit vectors in x and y directions, respectively. If v...

The velocity field of a two-dimensional, incompressible flow is given by $\overrightarrow{V} = \ 2sin{h}\,x\,\hat{i} + v(x,y)\hat{j}$ where $ \hat{i}$ and $\underset{\dot{}}{j}$ de...

Consider an isentropic flow of air (ratio of specific heats = 1.4) through a duct as shown in the figure. The variations in the flow across the cross-section are negligible. The fl...

Consider a unidirectional fluid flow with the velocity field given by V(x, y, z, t) = u(x, t) î where u(0, t) = 1. If the spatially homogeneous density field varies with time t as...

Consider a unidirectional fluid flow with the velocity field given by V(𝑥, 𝑦, 𝑧, 𝑡) = 𝑢(𝑥, 𝑡) 𝑖̂ where 𝑢(0,𝑡) = 1. If the spatially homogeneous density field varies with...

Consider steady, one-dimensional compressible flow of a gas in a pipe of diameter 1 m. At one location in the pipe, the density and velocity are 1 kg/m 3 and 100 m/s, respectively....

For a two-dimensional incompressible flow field given by $\vec{u} = A(x\hat{i} - y \hat{j})$, where A > 0, which one of the following statements is FALSE?

For steady flow of a viscous incompressible fluid through a circular pipe of constant diameter, the average velocity in the fully developed region is constant. Which one of the fol...

The velocity field on an incompressible flow is given by $$V = \left( {{a_1}x + {a_2}y + {a_3}z} \right)i + \left( {{b_1}x + {b_2}y + {b_3}z} \right)j\,$$ $$ + \left( {{c_1}x + {c_...

For an incompressible flow field , $$\overrightarrow {V,} $$ which one of the following conditions must be satisfied?

Air enters an adiabatic nozzle at $$300$$ $$kPa,$$ $$500$$ $$K$$ with a velocity of $$10$$ $$m/s.$$ It leaves the nozzle at $$100$$ $$kPa$$ with a velocity of $$180$$ $$m/s.$$ The...

For a continuity equation given $$\nabla .\overrightarrow V = 0$$ to be valid, $$\overrightarrow V $$ where is the velocity vector, which one of the folllowing is a necessary condi...

A venturimeter of $$20$$ $$mm$$ throat diameter is used to measure the velocity of water in a horizontal pipe of $$40$$ $$mm$$ diameter. If the pressure difference between the pipe...

The $$2$$ - $$D$$ flow with, velocity $$\overrightarrow v = \left( {x + 2y + 2} \right)\overrightarrow i + \left( {4 - y} \right)\overrightarrow j $$ is

The velocity components in the $$x$$ and $$y$$ directions are given by $$u = \lambda x{y^3} - {x^2}y,$$ $$v = x{y^2} - {3 \over 4}{y^4}.$$ The value of $$\lambda $$ for a possible...