1
GATE ME 2024
+1
-0.33

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 $\underset{\dot{}}{j}$ denote the unit vectors in x and y directions, respectively. If $v(x, 0) = cosh\ x$, then $v(0,-1)$ is

A

1

B

2

C

3

D

4

2
GATE ME 2017 Set 1
+1
-0.3
Consider the two-dimensional velocity field given by
$$\overrightarrow V = \left( {5 + {a_1}x + {b_1}y} \right)\widehat i + \left( {4 + {a_2}x + {b_2}y} \right)\widehat j,$$
where $${a_1},\,\,{b_1},\,\,{a_2}$$ and $${b^2}$$ are constants. Which one of the following conditions needs to be satisfied for the flow to be incompressible?
A
$${a_1} + {b_1} = 0$$
B
$${a_1} + {b_2} = 0$$
C
$${a_2} + {b_2} = 0$$
D
$${a_2} + {b_1} = 0$$
3
GATE ME 2016 Set 3
+1
-0.3
For a certain two-dimensional incompressible flow, velocity field is given by $$2xy\widehat i - {y^2}\widehat j.$$ The streamlines for this flow are given by the family of curves
A
$${x^2}{y^2} =$$ constant
B
$$x{y^2} =$$ constant
C
$$2xy - {y^2}$$ $$=$$ constant
D
$$xy =$$ constant
4
GATE ME 2016 Set 3
Fill in the Blanks
+1
-0
A channel of width $$450$$ $$mm$$ branches into two sub-channels having width $$300$$ $$mm$$ and $$200$$ $$mm$$ as shown in figure. If the volumetric flow rate (taking unit depth) of an incompressible flow through the main channel is $$0.9$$ $$3$$ $$m/s,$$ and the velocity in the sub-channel of width $$200$$ $$mm$$ is $$3$$ $$m/s,$$ the velocity in the sub-channel of width $$300$$ $$mm$$ is _____________ $$m/s$$.

Assume both inlet and outlet to be at the same elevation.

GATE ME Subjects
EXAM MAP
Medical
NEET