A steam function is given by ϕ = 6x – 5y. The magnitude of the resultant velocity at any point will be:

This question was previously asked in

PGCIL DT Civil 2018 Official Paper

- √32
- √61
- √56
- √82

Option 2 : √61

__Concept:__

Stream Function: It is the scalar function of space and time.

The partial derivative of stream function with respect to any direction gives the velocity component perpendicular to that direction.

\(u = - \frac{{\partial \psi }}{{\partial y}}\) & \(v = \frac{{\partial \psi }}{{\partial x}}\)

Stream function defines only for two-dimensional flow.

Properties of stream function:

- If ψ exists, it follows the continuity equation and the flow may be rotational or irrotational.
- If ψ satisfies the Laplace equation, then the flow is irrotational.

__Calculation____:__

Given:

ψ = 6x - 5y, \(u = \frac{{ - \partial {\rm{\Psi }}}}{{\partial y}} =~5,\;\nu = \frac{{\partial {\rm{\Psi }}}}{{\partial x}} =6\)

Resultant velocity \( = \sqrt {{u^2} + {\nu ^2}} = \sqrt {{5^2} + {6^2}} = \sqrt61\;m/s\)

India’s **#1 Learning** Platform

Start Complete Exam Preparation

Daily Live MasterClasses

Practice Question Bank

Mock Tests & Quizzes

Trusted by 2,17,23,979+ Students

Start your FREE coaching now >>

131 Total Tests 12 Free Tests

Start Free Test
130 Total Tests 8 Free Tests

Start Free Test
Testbook Edu Solutions Pvt. Ltd.

1st & 2nd Floor, Zion Building,

Plot No. 273, Sector 10, Kharghar,

Navi Mumbai - 410210

[email protected]
Plot No. 273, Sector 10, Kharghar,

Navi Mumbai - 410210

Toll Free:1800 833 0800

Office Hours: 10 AM to 7 PM (all 7 days)